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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 180708e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180708.c1 | 180708e1 | \([0, -1, 0, -321207557, 2215893745761]\) | \(-4075934708727808/13045131\) | \(-11730113180469224614656\) | \([]\) | \(30689280\) | \(3.4590\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 180708e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 180708e do not have complex multiplication.Modular form 180708.2.a.e
sage: E.q_eigenform(10)