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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 9408.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.da1 | 9408cv4 | \([0, 1, 0, -790337, 270174015]\) | \(7080974546692/189\) | \(1457236279296\) | \([2]\) | \(73728\) | \(1.8477\) | |
| 9408.da2 | 9408cv3 | \([0, 1, 0, -76897, -1010017]\) | \(6522128932/3720087\) | \(28682781685383168\) | \([2]\) | \(73728\) | \(1.8477\) | |
| 9408.da3 | 9408cv2 | \([0, 1, 0, -49457, 4198095]\) | \(6940769488/35721\) | \(68854414196736\) | \([2, 2]\) | \(36864\) | \(1.5011\) | |
| 9408.da4 | 9408cv1 | \([0, 1, 0, -1437, 135603]\) | \(-2725888/64827\) | \(-7809875684352\) | \([2]\) | \(18432\) | \(1.1546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.da have rank \(0\).
Complex multiplication
The elliptic curves in class 9408.da do not have complex multiplication.Modular form 9408.2.a.da
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
