Properties

Label 42978.n
Number of curves 11
Conductor 4297842978
CM no
Rank 11

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Copy content sage:E = EllipticCurve("n1") E.isogeny_class()
 

Elliptic curves in class 42978.n

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42978.n1 42978h1 [1,1,1,113988,818888349][1, 1, 1, 113988, 818888349] 163795088554066363967/289750937641750196352163795088554066363967/289750937641750196352 289750937641750196352-289750937641750196352 [][] 22680002268000 2.60532.6053 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curve 42978.n1 has rank 11.

Complex multiplication

The elliptic curves in class 42978.n do not have complex multiplication.

Modular form 42978.2.a.n

Copy content sage:E.q_eigenform(10)
 
q+q2q3+q4+2q5q63q7+q8+q9+2q10+6q11q12q133q142q15+q16q17+q18q19+O(q20)q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} + 2 q^{10} + 6 q^{11} - q^{12} - q^{13} - 3 q^{14} - 2 q^{15} + q^{16} - q^{17} + q^{18} - q^{19} + O(q^{20}) Copy content Toggle raw display