Properties

Label 270802.k
Number of curves $1$
Conductor $270802$
CM no
Rank $0$

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

Elliptic curves in class 270802.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.k1 270802k1 \([1, -1, 0, 9132157712, 117242784756992]\) \(5805798253576046271027/3769183309498679296\) \(-54680092480706364912736585908224\) \([]\) \(1830624768\) \(4.7788\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 270802.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 270802.k do not have complex multiplication.

Modular form 270802.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3q^{3} + q^{4} + 3q^{5} - 3q^{6} - q^{7} - q^{8} + 6q^{9} - 3q^{10} - 5q^{11} + 3q^{12} + q^{13} + q^{14} + 9q^{15} + q^{16} - 2q^{17} - 6q^{18} + 4q^{19} + O(q^{20})\)  Toggle raw display