Properties

Label 4012.c
Number of curves 1
Conductor 4012
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("4012.c1")
sage: E.isogeny_class()

Elliptic curves in class 4012.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4012.c1 4012b1 [0, -1, 0, 3, -26] 1 288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 4012.c1 has rank \(1\).

Modular form 4012.2.a.c

sage: E.q_eigenform(10)
\( q - q^{3} - 3q^{5} + q^{7} - 2q^{9} + 2q^{11} - 2q^{13} + 3q^{15} - q^{17} + q^{19} + O(q^{20}) \)