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Properties

Label 3234.j
Number of curves $1$
Conductor $3234$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, 0, 1, -271, -4798]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 3234.j1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(7\)\(1\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(17\) \( 1 - T + 17 T^{2}\) 1.17.ab
\(19\) \( 1 - 3 T + 19 T^{2}\) 1.19.ad
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 + T + 29 T^{2}\) 1.29.b
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 3234.j do not have complex multiplication.

Modular form 3234.2.a.j

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

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

Elliptic curves in class 3234.j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3234.j1 3234l1 \([1, 0, 1, -271, -4798]\) \(-44681709625/175177728\) \(-8583708672\) \([]\) \(1920\) \(0.59153\) \(\Gamma_0(N)\)-optimal