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Properties

Label 320790t
Number of curves $2$
Conductor $320790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 320790t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.t1 320790t1 \([1, 0, 1, -4348734, -2297038928]\) \(376806661463714041/123655521818880\) \(2984743690134221502720\) \([2]\) \(37158912\) \(2.8237\) \(\Gamma_0(N)\)-optimal
320790.t2 320790t2 \([1, 0, 1, 12505746, -15767139344]\) \(8961052973061164039/9635727199827600\) \(-232583030151015483104400\) \([2]\) \(74317824\) \(3.1703\)  

Rank

sage: E.rank()
 

The elliptic curves in class 320790t have rank \(1\).

Complex multiplication

The elliptic curves in class 320790t do not have complex multiplication.

Modular form 320790.2.a.t

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.