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Properties

Label 46090g
Number of curves $2$
Conductor $46090$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 46090g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46090.h2 46090g1 \([1, 0, 0, -70032436, 225572278416]\) \(37985811754890582644789153089/119762800816947200\) \(119762800816947200\) \([3]\) \(4504896\) \(2.9267\) \(\Gamma_0(N)\)-optimal
46090.h1 46090g2 \([1, 0, 0, -72500276, 208820340880]\) \(42144673353901398176116477249/5550424680603960608000000\) \(5550424680603960608000000\) \([]\) \(13514688\) \(3.4760\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46090g have rank \(0\).

Complex multiplication

The elliptic curves in class 46090g do not have complex multiplication.

Modular form 46090.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - q^{5} - 2 q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} - q^{11} - 2 q^{12} - q^{13} - 4 q^{14} + 2 q^{15} + q^{16} + 3 q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.