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SageMath
E = EllipticCurve("jc1")
E.isogeny_class()
Elliptic curves in class 346800jc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346800.jc6 | 346800jc1 | \([0, 1, 0, -9250408, -13308260812]\) | \(-56667352321/16711680\) | \(-25816277062778880000000\) | \([2]\) | \(21233664\) | \(3.0149\) | \(\Gamma_0(N)\)-optimal |
| 346800.jc5 | 346800jc2 | \([0, 1, 0, -157218408, -758771044812]\) | \(278202094583041/16646400\) | \(25715432230502400000000\) | \([2, 2]\) | \(42467328\) | \(3.3615\) | |
| 346800.jc4 | 346800jc3 | \([0, 1, 0, -166466408, -664496932812]\) | \(330240275458561/67652010000\) | \(104509123799276160000000000\) | \([2, 2]\) | \(84934656\) | \(3.7081\) | |
| 346800.jc2 | 346800jc4 | \([0, 1, 0, -2515458408, -48560295844812]\) | \(1139466686381936641/4080\) | \(6302802017280000000\) | \([2]\) | \(84934656\) | \(3.7081\) | |
| 346800.jc3 | 346800jc5 | \([0, 1, 0, -834634408, 8691191403188]\) | \(41623544884956481/2962701562500\) | \(4576794457040100000000000000\) | \([2, 2]\) | \(169869312\) | \(4.0546\) | |
| 346800.jc7 | 346800jc6 | \([0, 1, 0, 353733592, -3986494132812]\) | \(3168685387909439/6278181696900\) | \(-9698562809821493510400000000\) | \([2]\) | \(169869312\) | \(4.0546\) | |
| 346800.jc1 | 346800jc7 | \([0, 1, 0, -13117134408, 578230716403188]\) | \(161572377633716256481/914742821250\) | \(1413098749771298640000000000\) | \([2]\) | \(339738624\) | \(4.4012\) | |
| 346800.jc8 | 346800jc8 | \([0, 1, 0, 757177592, 37926410595188]\) | \(31077313442863199/420227050781250\) | \(-649168603769531250000000000000\) | \([2]\) | \(339738624\) | \(4.4012\) |
Rank
sage: E.rank()
The elliptic curves in class 346800jc have rank \(1\).
Complex multiplication
The elliptic curves in class 346800jc do not have complex multiplication.Modular form 346800.2.a.jc
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
