Properties

Label 180708m
Number of curves $1$
Conductor $180708$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 180708m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180708.k1 180708m1 \([0, -1, 0, -16884, -47611944]\) \(-592/1089\) \(-979223072081912064\) \([]\) \(2493504\) \(2.1311\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 180708m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 180708m do not have complex multiplication.

Modular form 180708.2.a.m

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