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Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 320790e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.e1 320790e1 \([1, 1, 0, -3448, 700552]\) \(-15693666935401/727542729000\) \(-210259848681000\) \([]\) \(1368576\) \(1.4283\) \(\Gamma_0(N)\)-optimal
320790.e2 320790e2 \([1, 1, 0, 30977, -18735803]\) \(11374230639551399/532029028170240\) \(-153756389141199360\) \([]\) \(4105728\) \(1.9776\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 320790.2.a.e

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