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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 174.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
174.a1 | 174e1 | \([1, 1, 0, -56, -192]\) | \(-19968681097/712704\) | \(-712704\) | \([]\) | \(52\) | \(-0.10484\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 174.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 174.a do not have complex multiplication.Modular form 174.2.a.a
sage: E.q_eigenform(10)