Properties

Label 707.a
Number of curves $1$
Conductor $707$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 707.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
707.a1 707a1 \([0, 1, 1, -12, 12]\) \(207474688/4949\) \(4949\) \([]\) \(104\) \(-0.50615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 707.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 707.a do not have complex multiplication.

Modular form 707.2.a.a

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