Properties

Label 270802.d
Number of curves $1$
Conductor $270802$
CM no
Rank $2$

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.d1 270802d1 \([1, 1, 0, 215, -1777]\) \(1297427375/2540258\) \(-2136356978\) \([]\) \(101760\) \(0.47472\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 270802.d1 has rank \(2\).

Complex multiplication

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

Modular form 270802.2.a.d

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