Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3380.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.e1 3380g1 \([0, -1, 0, -30, 25]\) \(1141504/625\) \(1690000\) \([]\) \(576\) \(-0.11425\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3380.e1 has rank \(1\).

Complex multiplication

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

Modular form 3380.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 5 q^{7} - 2 q^{9} + 5 q^{11} - q^{15} - q^{17} + 3 q^{19} + O(q^{20})\)  Toggle raw display