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Properties

Label 246202.a
Number of curves $1$
Conductor $246202$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, -1, 0, -2682478, 1953691348]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 246202.a1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(11\)\(1 - T\)
\(19\)\(1\)
\(31\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T + 3 T^{2}\) 1.3.d
\(5\) \( 1 - 3 T + 5 T^{2}\) 1.5.ad
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 3 T + 17 T^{2}\) 1.17.d
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 246202.a do not have complex multiplication.

Modular form 246202.2.a.a

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} - q^{8} + 6 q^{9} - 3 q^{10} + q^{11} - 3 q^{12} + 2 q^{13} - 2 q^{14} - 9 q^{15} + q^{16} - 3 q^{17} - 6 q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 246202.a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
246202.a1 246202a1 \([1, -1, 0, -2682478, 1953691348]\) \(-45374380016993217/8766492948224\) \(-412427384029485465344\) \([]\) \(20736000\) \(2.6793\) \(\Gamma_0(N)\)-optimal