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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1530c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1530.b6 | 1530c1 | \([1, -1, 0, -720, -8960]\) | \(-56667352321/16711680\) | \(-12182814720\) | \([2]\) | \(1024\) | \(0.64975\) | \(\Gamma_0(N)\)-optimal |
| 1530.b5 | 1530c2 | \([1, -1, 0, -12240, -518144]\) | \(278202094583041/16646400\) | \(12135225600\) | \([2, 2]\) | \(2048\) | \(0.99633\) | |
| 1530.b2 | 1530c3 | \([1, -1, 0, -195840, -33309104]\) | \(1139466686381936641/4080\) | \(2974320\) | \([2]\) | \(4096\) | \(1.3429\) | |
| 1530.b4 | 1530c4 | \([1, -1, 0, -12960, -453200]\) | \(330240275458561/67652010000\) | \(49318315290000\) | \([2, 2]\) | \(4096\) | \(1.3429\) | |
| 1530.b3 | 1530c5 | \([1, -1, 0, -64980, 5986876]\) | \(41623544884956481/2962701562500\) | \(2159809439062500\) | \([2, 2]\) | \(8192\) | \(1.6895\) | |
| 1530.b7 | 1530c6 | \([1, -1, 0, 27540, -2745500]\) | \(3168685387909439/6278181696900\) | \(-4576794457040100\) | \([2]\) | \(8192\) | \(1.6895\) | |
| 1530.b1 | 1530c7 | \([1, -1, 0, -1021230, 397475626]\) | \(161572377633716256481/914742821250\) | \(666847516691250\) | \([2]\) | \(16384\) | \(2.0360\) | |
| 1530.b8 | 1530c8 | \([1, -1, 0, 58950, 26038750]\) | \(31077313442863199/420227050781250\) | \(-306345520019531250\) | \([2]\) | \(16384\) | \(2.0360\) |
Rank
sage: E.rank()
The elliptic curves in class 1530c have rank \(0\).
Complex multiplication
The elliptic curves in class 1530c do not have complex multiplication.Modular form 1530.2.a.c
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
