Label 1728.k
Number of curves $1$
Conductor $1728$
CM no
Rank $1$

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

Elliptic curves in class 1728.k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1728.k1 1728y1 \([0, 0, 0, -108, 1296]\) \(-216\) \(-644972544\) \([]\) \(576\) \(0.37510\) \(\Gamma_0(N)\)-optimal


sage: E.rank()

The elliptic curve 1728.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1728.k do not have complex multiplication.

Modular form 1728.2.a.k

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