Properties

Label 35378.j
Number of curves $1$
Conductor $35378$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 35378.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35378.j1 35378l1 \([1, -1, 1, -1029279, 342492483]\) \(25137/4\) \(19189744795654688836\) \([]\) \(1666224\) \(2.4226\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 35378.j1 has rank \(1\).

Complex multiplication

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

Modular form 35378.2.a.j

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