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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 50820b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50820.c1 | 50820b1 | \([0, -1, 0, -694701, -222693975]\) | \(-81756451446784/24958395\) | \(-11319121716376320\) | \([]\) | \(518400\) | \(2.0576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50820b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 50820b do not have complex multiplication.Modular form 50820.2.a.b
sage: E.q_eigenform(10)