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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2904.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2904.c1 | 2904d5 | \([0, -1, 0, -46504, 3875500]\) | \(3065617154/9\) | \(32653412352\) | \([2]\) | \(5120\) | \(1.2467\) | |
| 2904.c2 | 2904d3 | \([0, -1, 0, -7784, -261732]\) | \(28756228/3\) | \(5442235392\) | \([2]\) | \(2560\) | \(0.90017\) | |
| 2904.c3 | 2904d4 | \([0, -1, 0, -2944, 59644]\) | \(1556068/81\) | \(146940355584\) | \([2, 2]\) | \(2560\) | \(0.90017\) | |
| 2904.c4 | 2904d2 | \([0, -1, 0, -524, -3276]\) | \(35152/9\) | \(4081676544\) | \([2, 2]\) | \(1280\) | \(0.55360\) | |
| 2904.c5 | 2904d1 | \([0, -1, 0, 81, -372]\) | \(2048/3\) | \(-85034928\) | \([2]\) | \(640\) | \(0.20702\) | \(\Gamma_0(N)\)-optimal |
| 2904.c6 | 2904d6 | \([0, -1, 0, 1896, 231948]\) | \(207646/6561\) | \(-23804337604608\) | \([2]\) | \(5120\) | \(1.2467\) |
Rank
sage: E.rank()
The elliptic curves in class 2904.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2904.c do not have complex multiplication.Modular form 2904.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
