Properties

Label 311696.o
Number of curves $1$
Conductor $311696$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 311696.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.o1 311696o1 \([0, 1, 0, -6304408832, -192728787183308]\) \(-31561336767775878870433/10701003643411522\) \(-9395630762306014734036508672\) \([]\) \(372252672\) \(4.3394\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 311696.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 311696.o do not have complex multiplication.

Modular form 311696.2.a.o

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{5} + q^{7} + q^{9} - 5 q^{13} - 4 q^{15} - 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display