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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 37440.dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.dr1 | 37440cs2 | \([0, 0, 0, -381252, -90443104]\) | \(2052450196928704/4317958125\) | \(12893353873920000\) | \([2]\) | \(294912\) | \(1.9764\) | |
| 37440.dr2 | 37440cs1 | \([0, 0, 0, -15627, -2400604]\) | \(-9045718037056/48125390625\) | \(-2245338225000000\) | \([2]\) | \(147456\) | \(1.6298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.dr have rank \(0\).
Complex multiplication
The elliptic curves in class 37440.dr do not have complex multiplication.Modular form 37440.2.a.dr
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
