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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 163254dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 163254.w1 | 163254dm1 | \([1, 1, 0, -630184779, 6089844573207]\) | \(-200767734417067658737/40112050308498\) | \(-5529786760500749468432802\) | \([]\) | \(68140800\) | \(3.7462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 163254dm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 163254dm do not have complex multiplication.Modular form 163254.2.a.dm
sage: E.q_eigenform(10)