Properties

Label 51376.t
Number of curves $1$
Conductor $51376$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 51376.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51376.t1 51376m1 \([0, 1, 0, -2706760, -1799597708]\) \(-110931033861649/6497214464\) \(-128453891071038980096\) \([]\) \(1257984\) \(2.6145\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51376.t1 has rank \(2\).

Complex multiplication

The elliptic curves in class 51376.t do not have complex multiplication.

Modular form 51376.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 3 q^{7} - 2 q^{9} - 4 q^{11} + q^{15} - 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display