Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3675.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.p1 3675m1 \([0, 1, 1, -380158, -148802531]\) \(-1376628736/1366875\) \(-6032943062138671875\) \([]\) \(112896\) \(2.2994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3675.p1 has rank \(1\).

Complex multiplication

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

Modular form 3675.2.a.p

sage: E.q_eigenform(10)
 
\(q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{9} - 6q^{11} + 2q^{12} - 3q^{13} - 4q^{16} - 4q^{17} + 2q^{18} - q^{19} + O(q^{20})\)  Toggle raw display