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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 212160dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212160.q1 | 212160dm1 | \([0, -1, 0, -21, 51]\) | \(-16777216/3315\) | \(-212160\) | \([]\) | \(24192\) | \(-0.25487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 212160dm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 212160dm do not have complex multiplication.Modular form 212160.2.a.dm
sage: E.q_eigenform(10)