Properties

Label 3344.e
Number of curves $1$
Conductor $3344$
CM no
Rank $1$

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

Elliptic curves in class 3344.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3344.e1 3344b1 \([0, -1, 0, -5192, -142832]\) \(-7559297810066/33659659\) \(-68934981632\) \([]\) \(2880\) \(0.93204\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3344.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3344.e do not have complex multiplication.

Modular form 3344.2.a.e

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