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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 15680dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.cy1 | 15680dm1 | \([0, 1, 0, 42075, 10431875]\) | \(12459008/78125\) | \(-51652616960000000\) | \([]\) | \(100352\) | \(1.8888\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15680dm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 15680dm do not have complex multiplication.Modular form 15680.2.a.dm
sage: E.q_eigenform(10)