Properties

Label 53312.w
Number of curves $1$
Conductor $53312$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 53312.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.w1 53312u1 \([0, -1, 0, 47, 113]\) \(14000/17\) \(-13647872\) \([]\) \(9216\) \(0.055248\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53312.w do not have complex multiplication.

Modular form 53312.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{9} + 5 q^{11} - 5 q^{13} + q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display