Properties

Label 141570p
Number of curves $1$
Conductor $141570$
CM no
Rank $1$

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

Elliptic curves in class 141570p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.em1 141570p1 \([1, -1, 1, 75118, 93073731]\) \(27270901/2193750\) \(-3770933107658681250\) \([]\) \(2787840\) \(2.2440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 141570p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 141570p do not have complex multiplication.

Modular form 141570.2.a.p

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