Properties

Label 41070p
Number of curves $1$
Conductor $41070$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 41070p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.l1 41070p1 \([1, 0, 1, -384718, 120745856]\) \(-2454365649169/1035763200\) \(-2657484995710348800\) \([]\) \(1378944\) \(2.2432\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41070p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 41070p do not have complex multiplication.

Modular form 41070.2.a.p

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