Properties

Label 15680.u
Number of curves $1$
Conductor $15680$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 15680.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.u1 15680de1 \([0, 1, 0, -47105, -4592897]\) \(-15298178/3125\) \(-2361262489600000\) \([]\) \(80640\) \(1.6721\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 15680.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 15680.u do not have complex multiplication.

Modular form 15680.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} + q^{9} - q^{11} + 3 q^{13} - 2 q^{15} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display