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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 162240dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.dx1 | 162240dc1 | \([0, -1, 0, -128665, -18198233]\) | \(-762549907456/24024195\) | \(-7421452841200320\) | \([]\) | \(1128960\) | \(1.8216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162240dc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162240dc do not have complex multiplication.Modular form 162240.2.a.dc
sage: E.q_eigenform(10)