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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 421400f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
421400.f1 | 421400f1 | \([0, 1, 0, -408, 1368688]\) | \(-2/215\) | \(-809425120000000\) | \([]\) | \(1774080\) | \(1.5395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 421400f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 421400f do not have complex multiplication.Modular form 421400.2.a.f
sage: E.q_eigenform(10)