Properties

Label 2310.t
Number of curves $4$
Conductor $2310$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2310.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.t1 2310u3 \([1, 0, 0, -24261, -1456515]\) \(1579250141304807889/41926500\) \(41926500\) \([2]\) \(5184\) \(0.97671\)  
2310.t2 2310u4 \([1, 0, 0, -24231, -1460289]\) \(-1573398910560073969/8138108343750\) \(-8138108343750\) \([2]\) \(10368\) \(1.3233\)  
2310.t3 2310u1 \([1, 0, 0, -321, -1719]\) \(3658671062929/880165440\) \(880165440\) \([6]\) \(1728\) \(0.42740\) \(\Gamma_0(N)\)-optimal
2310.t4 2310u2 \([1, 0, 0, 759, -10575]\) \(48351870250991/76871856600\) \(-76871856600\) \([6]\) \(3456\) \(0.77398\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.t

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.