Properties

Label 10002d
Number of curves $1$
Conductor $10002$
CM no
Rank $1$

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

Elliptic curves in class 10002d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10002.d1 10002d1 \([1, 1, 1, -354, 2415]\) \(4906933498657/2560512\) \(2560512\) \([]\) \(2736\) \(0.18028\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10002d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10002d do not have complex multiplication.

Modular form 10002.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} - 2 q^{10} + 3 q^{11} - q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display