Properties

Label 100005.a
Number of curves 1
Conductor 100005
CM no
Rank 2

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Show commands for: SageMath

sage: E = EllipticCurve("100005.a1")
sage: E.isogeny_class()

Elliptic curves in class 100005.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100005.a1 100005a1 [0, -1, 1, -346, 2652] 1 53088 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 100005.a1 has rank \(2\).

Modular form None

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