Properties

Label 14157m
Number of curves $1$
Conductor $14157$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 14157m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14157.e1 14157m1 \([1, -1, 1, -20714, 727620]\) \(6289657/2197\) \(343319970475053\) \([]\) \(47520\) \(1.4906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 14157m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 14157m do not have complex multiplication.

Modular form 14157.2.a.m

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