Properties

Label 3675.e
Number of curves $1$
Conductor $3675$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3675.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.e1 3675b1 \([1, 1, 1, -393, -9654]\) \(-46585/243\) \(-35021166075\) \([]\) \(2520\) \(0.70751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3675.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3675.e do not have complex multiplication.

Modular form 3675.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3q^{8} + q^{9} + q^{12} + 3q^{13} - q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20})\)  Toggle raw display