Properties

Label 9225.bb
Number of curves $1$
Conductor $9225$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bb1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 9225.bb1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1\)
\(5\)\(1\)
\(41\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 - 2 T + 2 T^{2}\) 1.2.ac
\(7\) \( 1 + 4 T + 7 T^{2}\) 1.7.e
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 5 T + 17 T^{2}\) 1.17.af
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 2 T + 23 T^{2}\) 1.23.ac
\(29\) \( 1 + 5 T + 29 T^{2}\) 1.29.f
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 9225.bb do not have complex multiplication.

Modular form 9225.2.a.bb

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - 4 q^{7} + 2 q^{13} - 8 q^{14} - 4 q^{16} + 5 q^{17} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 9225.bb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9225.bb1 9225be1 \([0, 0, 1, -42375, 3435781]\) \(-29550530560/807003\) \(-229806713671875\) \([]\) \(47520\) \(1.5370\) \(\Gamma_0(N)\)-optimal