Properties

Label 5824.d
Number of curves $1$
Conductor $5824$
CM no
Rank $1$

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

Elliptic curves in class 5824.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5824.d1 5824bc1 \([0, 1, 0, -21, -77]\) \(-65536/91\) \(-1490944\) \([]\) \(768\) \(-0.12303\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5824.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5824.d do not have complex multiplication.

Modular form 5824.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{7} + q^{9} - 4 q^{11} - q^{13} + 2 q^{15} - 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display