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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 242550dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242550.dw1 | 242550dw1 | \([1, -1, 0, -53686467, -156949074059]\) | \(-260607143968297/11270993184\) | \(-740106232738231936500000\) | \([]\) | \(50803200\) | \(3.3458\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 242550dw1 has rank \(1\).
Complex multiplication
The elliptic curves in class 242550dw do not have complex multiplication.Modular form 242550.2.a.dw
sage: E.q_eigenform(10)