Properties

Label 2310o
Number of curves $6$
Conductor $2310$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.o5 2310o1 \([1, 1, 1, -332850, 86465727]\) \(-4078208988807294650401/880065599546327040\) \(-880065599546327040\) \([4]\) \(46080\) \(2.1643\) \(\Gamma_0(N)\)-optimal
2310.o4 2310o2 \([1, 1, 1, -5575730, 5065104575]\) \(19170300594578891358373921/671785075055001600\) \(671785075055001600\) \([2, 4]\) \(92160\) \(2.5109\)  
2310.o3 2310o3 \([1, 1, 1, -5826610, 4584017087]\) \(21876183941534093095979041/3572502915711058560000\) \(3572502915711058560000\) \([2, 2]\) \(184320\) \(2.8574\)  
2310.o1 2310o4 \([1, 1, 1, -89210930, 324283935935]\) \(78519570041710065450485106721/96428056919040\) \(96428056919040\) \([4]\) \(184320\) \(2.8574\)  
2310.o2 2310o5 \([1, 1, 1, -26238610, -47360440513]\) \(1997773216431678333214187041/187585177195046990066400\) \(187585177195046990066400\) \([2]\) \(368640\) \(3.2040\)  
2310.o6 2310o6 \([1, 1, 1, 10571310, 25743893055]\) \(130650216943167617311657439/361816948816603087500000\) \(-361816948816603087500000\) \([2]\) \(368640\) \(3.2040\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.o

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.