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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 82110.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82110.h1 | 82110l1 | \([1, 1, 0, -192397, 70948309]\) | \(-787629777366448036441/1723654824447591000\) | \(-1723654824447591000\) | \([]\) | \(1198080\) | \(2.1880\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82110.h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 82110.h do not have complex multiplication.Modular form 82110.2.a.h
sage: E.q_eigenform(10)