Properties

Label 3744.e
Number of curves $1$
Conductor $3744$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 3744.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.e1 3744g1 \([0, 0, 0, -3, -106]\) \(-8/13\) \(-4852224\) \([]\) \(480\) \(-0.038107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3744.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3744.e do not have complex multiplication.

Modular form 3744.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3 q^{7} + 2 q^{11} + q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display