Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 12675f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12675.i1 12675f1 \([1, 1, 1, 50612, 31877906]\) \(304175/9477\) \(-446715516533203125\) \([]\) \(120960\) \(2.0667\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12675f1 has rank \(1\).

Complex multiplication

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

Modular form 12675.2.a.f

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