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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 12705a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12705.h1 | 12705a1 | \([0, -1, 1, -15891, -2487013]\) | \(-250523582464/1369738755\) | \(-2426575758546555\) | \([]\) | \(48000\) | \(1.6362\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12705a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12705a do not have complex multiplication.Modular form 12705.2.a.a
sage: E.q_eigenform(10)