Properties

Label 281775m
Number of curves $1$
Conductor $281775$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 281775m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.m1 281775m1 \([1, 1, 1, -4919653, 4201417556]\) \(-15101696859749/14414517\) \(-12569021777646374625\) \([]\) \(9870336\) \(2.5865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 281775m1 has rank \(2\).

Complex multiplication

The elliptic curves in class 281775m do not have complex multiplication.

Modular form 281775.2.a.m

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