Properties

Label 1007a
Number of curves 1
Conductor 1007
CM no
Rank 1

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("1007.a1")
sage: E.isogeny_class()

Elliptic curves in class 1007a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1007.a1 1007a1 [0, 0, 1, 61, -105] 1 276 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1007a1 has rank \(1\).

Modular form 1007.2.a.a

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