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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 21160.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21160.h1 | 21160g1 | \([0, -1, 0, -4201, -103299]\) | \(60560505856/78125\) | \(10580000000\) | \([]\) | \(18816\) | \(0.83102\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21160.h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21160.h do not have complex multiplication.Modular form 21160.2.a.h
sage: E.q_eigenform(10)