Properties

Label 3136c
Number of curves 11
Conductor 31363136
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 3136c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.b1 3136c1 [0,0,0,1372,19208][0, 0, 0, -1372, -19208] 4838448384 59031562245903156224 [][] 26882688 0.665170.66517 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3136c1 has rank 11.

Complex multiplication

The elliptic curves in class 3136c do not have complex multiplication.

Modular form 3136.2.a.c

sage: E.q_eigenform(10)
 
q3q3+q5+6q9+q112q133q15+3q175q19+O(q20)q - 3 q^{3} + q^{5} + 6 q^{9} + q^{11} - 2 q^{13} - 3 q^{15} + 3 q^{17} - 5 q^{19} + O(q^{20}) Copy content Toggle raw display