Properties

Label 412224.d
Number of curves $1$
Conductor $412224$
CM no
Rank $0$

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

Elliptic curves in class 412224.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.d1 412224d1 \([0, -1, 0, -417, -551391]\) \(-30664297/501264384\) \(-131403450679296\) \([]\) \(1216512\) \(1.3880\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 412224.d do not have complex multiplication.

Modular form 412224.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - q^{7} + q^{9} - 4 q^{11} + q^{13} + 3 q^{15} + 7 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display