Properties

Label 3380.a
Number of curves $1$
Conductor $3380$
CM no
Rank $2$

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

Elliptic curves in class 3380.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.a1 3380d1 \([0, 0, 0, -13, 13]\) \(89856/25\) \(67600\) \([]\) \(576\) \(-0.36595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3380.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 3380.a do not have complex multiplication.

Modular form 3380.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - q^{5} - 3 q^{7} + 6 q^{9} - 3 q^{11} + 3 q^{15} - 7 q^{17} - q^{19} + O(q^{20})\)  Toggle raw display