Properties

Label 350350.bb
Number of curves $1$
Conductor $350350$
CM no
Rank $1$

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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 350350.bb1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
\(11\)\(1 + T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + T + 3 T^{2}\) 1.3.b
\(17\) \( 1 + 5 T + 17 T^{2}\) 1.17.f
\(19\) \( 1 - 3 T + 19 T^{2}\) 1.19.ad
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 - T + 29 T^{2}\) 1.29.ab
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 350350.bb do not have complex multiplication.

Modular form 350350.2.a.bb

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} - 2 q^{9} - q^{11} - q^{12} + q^{13} + q^{16} - 5 q^{17} + 2 q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 350350.bb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350350.bb1 350350bb1 \([1, 1, 0, -1146625, -473096875]\) \(-90694355177089/7436000\) \(-13669343187500000\) \([]\) \(4354560\) \(2.1409\) \(\Gamma_0(N)\)-optimal