Properties

Label 67.a
Number of curves 1
Conductor 67
CM no
Rank 0

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Show commands for: SageMath

sage: E = EllipticCurve("67.a1")
sage: E.isogeny_class()

Elliptic curves in class 67.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
67.a1 67a1 [0, 1, 1, -12, -21] 1 5 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 67.a1 has rank \(0\).

Modular form 67.2.a.a

sage: E.q_eigenform(10)
\( q + 2q^{2} - 2q^{3} + 2q^{4} + 2q^{5} - 4q^{6} - 2q^{7} + q^{9} + 4q^{10} - 4q^{11} - 4q^{12} + 2q^{13} - 4q^{14} - 4q^{15} - 4q^{16} + 3q^{17} + 2q^{18} + 7q^{19} + O(q^{20}) \)