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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 26010e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.w1 | 26010e1 | \([1, -1, 0, -472569, -257734675]\) | \(-85003587/160000\) | \(-21968613393792480000\) | \([]\) | \(470016\) | \(2.4012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 26010e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 26010e do not have complex multiplication.Modular form 26010.2.a.e
sage: E.q_eigenform(10)