Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 13005.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13005.h1 13005h1 \([0, 0, 1, -408, -3141]\) \(35651584/405\) \(85325805\) \([]\) \(4608\) \(0.33520\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13005.h1 has rank \(0\).

Complex multiplication

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

Modular form 13005.2.a.h

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