Properties

Label 12675g
Number of curves $1$
Conductor $12675$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 12675g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12675.k1 12675g1 \([1, 1, 1, -371888, 130109156]\) \(-4225/3\) \(-4038823003388671875\) \([]\) \(196560\) \(2.2701\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12675g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12675g do not have complex multiplication.

Modular form 12675.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{11} + q^{12} - 3 q^{14} - q^{16} - 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display