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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 75712.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.l1 | 75712cd2 | \([0, 1, 0, -5633, 90559]\) | \(125000/49\) | \(7750078988288\) | \([2]\) | \(138240\) | \(1.1718\) | |
| 75712.l2 | 75712cd1 | \([0, 1, 0, 1127, 10791]\) | \(8000/7\) | \(-138394267648\) | \([2]\) | \(69120\) | \(0.82527\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75712.l have rank \(0\).
Complex multiplication
The elliptic curves in class 75712.l do not have complex multiplication.Modular form 75712.2.a.l
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.
