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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 44100dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.i1 | 44100dr1 | \([0, 0, 0, -110231625, 445459030625]\) | \(-805661175040/729\) | \(-134034757860543750000\) | \([]\) | \(3870720\) | \(3.1604\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 44100dr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 44100dr do not have complex multiplication.Modular form 44100.2.a.dr
sage: E.q_eigenform(10)