Properties

Label 12844d
Number of curves $1$
Conductor $12844$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 12844d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12844.g1 12844d1 \([0, -1, 0, -3605, -82447]\) \(-4194304/19\) \(-23477598976\) \([]\) \(12960\) \(0.84154\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12844d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12844d do not have complex multiplication.

Modular form 12844.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + 3 q^{7} + q^{9} - 5 q^{11} + 2 q^{15} - 3 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display