Properties

Label 35378b
Number of curves $1$
Conductor $35378$
CM no
Rank $2$

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

Elliptic curves in class 35378b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35378.a1 35378b1 \([1, -1, 0, -58, 160]\) \(25137/4\) \(3467044\) \([]\) \(12528\) \(-0.022556\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35378b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 35378b do not have complex multiplication.

Modular form 35378.2.a.b

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