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Properties

Label 31790t
Number of curves $2$
Conductor $31790$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 31790t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31790.p1 31790t1 \([1, 1, 1, -295, 5205]\) \(-117649/440\) \(-10620530360\) \([]\) \(20160\) \(0.60950\) \(\Gamma_0(N)\)-optimal
31790.p2 31790t2 \([1, 1, 1, 2595, -125423]\) \(80062991/332750\) \(-8031776084750\) \([]\) \(60480\) \(1.1588\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31790t have rank \(0\).

Complex multiplication

The elliptic curves in class 31790t do not have complex multiplication.

Modular form 31790.2.a.t

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