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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 35574.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35574.e1 | 35574a1 | \([1, 1, 0, -409763, -101133171]\) | \(-991656390179/31104\) | \(-238659440874624\) | \([]\) | \(282240\) | \(1.8550\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 35574.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 35574.e do not have complex multiplication.Modular form 35574.2.a.e
sage: E.q_eigenform(10)