Properties

Label 3952.f
Number of curves $1$
Conductor $3952$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("f1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 3952.f1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(13\)\(1 + T\)
\(19\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(17\) \( 1 - T + 17 T^{2}\) 1.17.ab
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 3952.f do not have complex multiplication.

Modular form 3952.2.a.f

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

Elliptic curves in class 3952.f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3952.f1 3952b1 \([0, 0, 0, 1, -3]\) \(6912/247\) \(-3952\) \([]\) \(160\) \(-0.62992\) \(\Gamma_0(N)\)-optimal