Properties

Label 35083.a
Number of curves $1$
Conductor $35083$
CM no
Rank $3$

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

Elliptic curves in class 35083.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35083.a1 35083c1 \([0, 1, 1, -4, 8]\) \(-8998912/35083\) \(-35083\) \([]\) \(6096\) \(-0.44241\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35083.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 35083.a do not have complex multiplication.

Modular form 35083.2.a.a

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