Properties

Label 12705a
Number of curves $1$
Conductor $12705$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 12705a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12705.h1 12705a1 \([0, -1, 1, -15891, -2487013]\) \(-250523582464/1369738755\) \(-2426575758546555\) \([]\) \(48000\) \(1.6362\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12705a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 12705a do not have complex multiplication.

Modular form 12705.2.a.a

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