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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 190575.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.d1 | 190575c2 | \([0, 0, 1, -161535, 25114306]\) | \(-2887553024/16807\) | \(-2713212769372875\) | \([]\) | \(1620000\) | \(1.8024\) | |
| 190575.d2 | 190575c1 | \([0, 0, 1, 1815, -41594]\) | \(4096/7\) | \(-1130034472875\) | \([]\) | \(324000\) | \(0.99773\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.d have rank \(0\).
Complex multiplication
The elliptic curves in class 190575.d do not have complex multiplication.Modular form 190575.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
