Properties

Label 2310.p
Number of curves $2$
Conductor $2310$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 2310.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.p1 2310p1 \([1, 1, 1, -4995, -137955]\) \(13782741913468081/701662500\) \(701662500\) \([2]\) \(2880\) \(0.76742\) \(\Gamma_0(N)\)-optimal
2310.p2 2310p2 \([1, 1, 1, -4725, -153183]\) \(-11666347147400401/3126621093750\) \(-3126621093750\) \([2]\) \(5760\) \(1.1140\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2310.p have rank \(0\).

Complex multiplication

The elliptic curves in class 2310.p do not have complex multiplication.

Modular form 2310.2.a.p

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