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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 75810.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75810.cj1 | 75810cl4 | \([1, 1, 1, -32106445, -67588243693]\) | \(77799851782095807001/3092322318750000\) | \(145481027821556568750000\) | \([2]\) | \(8847360\) | \(3.2112\) | |
| 75810.cj2 | 75810cl2 | \([1, 1, 1, -5219165, 3168322355]\) | \(334199035754662681/101099003040000\) | \(4756291666238478240000\) | \([2, 2]\) | \(4423680\) | \(2.8646\) | |
| 75810.cj3 | 75810cl1 | \([1, 1, 1, -4757085, 3991009587]\) | \(253060782505556761/41184460800\) | \(1937559241845964800\) | \([4]\) | \(2211840\) | \(2.5180\) | \(\Gamma_0(N)\)-optimal |
| 75810.cj4 | 75810cl3 | \([1, 1, 1, 14274835, 21282147155]\) | \(6837784281928633319/8113766016106800\) | \(-381719270455604596090800\) | \([2]\) | \(8847360\) | \(3.2112\) |
Rank
sage: E.rank()
The elliptic curves in class 75810.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 75810.cj do not have complex multiplication.Modular form 75810.2.a.cj
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.
