Properties

Label 3696a
Number of curves $1$
Conductor $3696$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 3696a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3696.c1 3696a1 \([0, -1, 0, -12, -549]\) \(-12967168/8251551\) \(-132024816\) \([]\) \(1344\) \(0.23728\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3696a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3696a do not have complex multiplication.

Modular form 3696.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - q^{7} + q^{9} - q^{11} - 3 q^{13} + 3 q^{15} + 4 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display