Properties

Label 180708k
Number of curves $1$
Conductor $180708$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 180708k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180708.i1 180708k1 \([0, -1, 0, 135075, 38548809]\) \(303104/891\) \(-801182513521564416\) \([]\) \(2685312\) \(2.1188\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 180708k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 180708k do not have complex multiplication.

Modular form 180708.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 4 q^{7} + q^{9} + q^{11} - q^{15} + 4 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display