Properties

Label 13005c
Number of curves $1$
Conductor $13005$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 13005c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13005.m1 13005c1 \([1, -1, 0, 19020, -688249]\) \(462866157/390625\) \(-642165563671875\) \([]\) \(48384\) \(1.5290\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13005c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 13005c do not have complex multiplication.

Modular form 13005.2.a.c

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