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SageMath
E = EllipticCurve("jn1")
E.isogeny_class()
Elliptic curves in class 141120.jn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.jn1 | 141120io3 | \([0, 0, 0, -875532, 175544656]\) | \(26410345352/10546875\) | \(29640771417600000000\) | \([2]\) | \(3538944\) | \(2.4345\) | |
| 141120.jn2 | 141120io2 | \([0, 0, 0, -399252, -95172896]\) | \(20034997696/455625\) | \(160060165655040000\) | \([2, 2]\) | \(1769472\) | \(2.0879\) | |
| 141120.jn3 | 141120io1 | \([0, 0, 0, -397047, -96296564]\) | \(1261112198464/675\) | \(3705096427200\) | \([2]\) | \(884736\) | \(1.7413\) | \(\Gamma_0(N)\)-optimal |
| 141120.jn4 | 141120io4 | \([0, 0, 0, 41748, -293975696]\) | \(2863288/13286025\) | \(-37338835444007731200\) | \([2]\) | \(3538944\) | \(2.4345\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.jn have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.jn do not have complex multiplication.Modular form 141120.2.a.jn
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
