Properties

Label 10005.j
Number of curves $1$
Conductor $10005$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 10005.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10005.j1 10005n1 \([0, 1, 1, -1305, 12506]\) \(245973316796416/69995230125\) \(69995230125\) \([]\) \(6720\) \(0.78766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10005.j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 10005.j do not have complex multiplication.

Modular form 10005.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} + q^{7} + q^{9} - 2 q^{12} + 4 q^{13} + q^{15} + 4 q^{16} + 7 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display