Properties

Label 34862.a
Number of curves $1$
Conductor $34862$
CM no
Rank $3$

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

Elliptic curves in class 34862.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34862.a1 34862a1 \([1, -1, 1, -57, 345]\) \(-20145851361/35698688\) \(-35698688\) \([]\) \(57728\) \(0.13954\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 34862.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 34862.a do not have complex multiplication.

Modular form 34862.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - 4 q^{5} - 3 q^{6} - 4 q^{7} + q^{8} + 6 q^{9} - 4 q^{10} - 4 q^{11} - 3 q^{12} - 6 q^{13} - 4 q^{14} + 12 q^{15} + q^{16} - 6 q^{17} + 6 q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display