Properties

Label 14157.a
Number of curves $1$
Conductor $14157$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 14157.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14157.a1 14157u1 \([0, 0, 1, -9075, 531220]\) \(-7744000000/6940323\) \(-74076073132347\) \([]\) \(61440\) \(1.3583\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 14157.a1 has rank \(2\).

Complex multiplication

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

Modular form 14157.2.a.a

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