Properties

Label 2925.t
Number of curves $1$
Conductor $2925$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("t1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 2925.t1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1\)
\(5\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 - 2 T + 2 T^{2}\) 1.2.ac
\(7\) \( 1 - 3 T + 7 T^{2}\) 1.7.ad
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(17\) \( 1 - 5 T + 17 T^{2}\) 1.17.af
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 2925.t do not have complex multiplication.

Modular form 2925.2.a.t

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 3 q^{7} + 5 q^{11} - q^{13} + 6 q^{14} - 4 q^{16} + 5 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 2925.t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2925.t1 2925h1 \([0, 0, 1, -75, 2281]\) \(-4096/195\) \(-2221171875\) \([]\) \(2304\) \(0.47344\) \(\Gamma_0(N)\)-optimal