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Properties

Label 2730.c
Number of curves $4$
Conductor $2730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 2730.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2730.c1 2730b3 \([1, 1, 0, -135893, -19338363]\) \(277536408914951281369/2063880\) \(2063880\) \([2]\) \(9216\) \(1.2626\)  
2730.c2 2730b4 \([1, 1, 0, -9093, -260043]\) \(83161039719198169/19757817763320\) \(19757817763320\) \([2]\) \(9216\) \(1.2626\)  
2730.c3 2730b2 \([1, 1, 0, -8493, -304803]\) \(67762119444423769/5843073600\) \(5843073600\) \([2, 2]\) \(4608\) \(0.91608\)  
2730.c4 2730b1 \([1, 1, 0, -493, -5603]\) \(-13293525831769/4892160000\) \(-4892160000\) \([2]\) \(2304\) \(0.56950\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2730.c have rank \(0\).

Complex multiplication

The elliptic curves in class 2730.c do not have complex multiplication.

Modular form 2730.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.