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Properties

Label 71094.bb
Number of curves $1$
Conductor $71094$
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 71094.bb1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(17\)\(1\)
\(41\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 3 T + 5 T^{2}\) 1.5.ad
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 4 T + 29 T^{2}\) 1.29.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 71094.bb do not have complex multiplication.

Modular form 71094.2.a.bb

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + 3 q^{10} + 2 q^{11} + q^{12} - 4 q^{13} + q^{14} + 3 q^{15} + q^{16} + q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 71094.bb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71094.bb1 71094x1 \([1, 0, 0, -7388019, -7794992799]\) \(-9077389327259968317569/88831108765974528\) \(-436427237367232856064\) \([]\) \(4334592\) \(2.7803\) \(\Gamma_0(N)\)-optimal