Properties

Label 3700.a
Number of curves $1$
Conductor $3700$
CM no
Rank $1$

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

Elliptic curves in class 3700.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3700.a1 3700e1 \([0, 0, 0, -5486200, 4920596500]\) \(4565397831743545344/27087483203125\) \(108349932812500000000\) \([]\) \(299520\) \(2.6842\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3700.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3700.a do not have complex multiplication.

Modular form 3700.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + 3 q^{7} + 6 q^{9} + 5 q^{11} - 2 q^{13} - 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display