Properties

Label 309465.d
Number of curves $1$
Conductor $309465$
CM no
Rank $1$

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

Elliptic curves in class 309465.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309465.d1 309465d1 \([0, 0, 1, -1587, -222048]\) \(-4096/195\) \(-21044041800795\) \([]\) \(1214400\) \(1.2365\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 309465.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 309465.d do not have complex multiplication.

Modular form 309465.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + q^{5} + 3 q^{7} - 2 q^{10} - 5 q^{11} + q^{13} - 6 q^{14} - 4 q^{16} + 5 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display