Properties

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

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 12675bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12675.l1 12675bj1 \([1, 0, 0, -6962888, -7071390483]\) \(117161545345/19683\) \(6271885852126171875\) \([]\) \(589680\) \(2.6143\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12675bj1 has rank \(1\).

Complex multiplication

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

Modular form 12675.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} - 4 q^{7} + 3 q^{8} + q^{9} + 5 q^{11} - q^{12} + 4 q^{14} - q^{16} + 2 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display