Properties

Label 356928.bh
Number of curves $1$
Conductor $356928$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bh1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 356928.bh1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(11\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(7\) \( 1 + 3 T + 7 T^{2}\) 1.7.d
\(17\) \( 1 + 4 T + 17 T^{2}\) 1.17.e
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 - T + 23 T^{2}\) 1.23.ab
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 356928.bh do not have complex multiplication.

Modular form 356928.2.a.bh

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 3 q^{7} + q^{9} - q^{11} + q^{15} - 4 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 356928.bh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
356928.bh1 356928bh1 \([0, -1, 0, -497761, -141964031]\) \(-10779215329/658944\) \(-833774375323828224\) \([]\) \(4644864\) \(2.1934\) \(\Gamma_0(N)\)-optimal