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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 53312.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.x1 | 53312bj1 | \([0, -1, 0, -14177, 817153]\) | \(-208537/68\) | \(-102762143547392\) | \([]\) | \(129024\) | \(1.4011\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53312.x do not have complex multiplication.Modular form 53312.2.a.x
sage: E.q_eigenform(10)