Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3380.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3380.b1 3380j1 \([0, 0, 0, -2197, 28561]\) \(89856/25\) \(326292288400\) \([]\) \(7488\) \(0.91652\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3380.b1 has rank \(1\).

Complex multiplication

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

Modular form 3380.2.a.b

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