Properties

Label 4730.c
Number of curves $4$
Conductor $4730$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4730.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4730.c1 4730b3 \([1, -1, 0, -137654, 17939460]\) \(288464247626448102201/28440150818750000\) \(28440150818750000\) \([4]\) \(30720\) \(1.8940\)  
4730.c2 4730b2 \([1, -1, 0, -31174, -1801932]\) \(3350496292255693881/524098606240000\) \(524098606240000\) \([2, 2]\) \(15360\) \(1.5474\)  
4730.c3 4730b1 \([1, -1, 0, -29894, -1981900]\) \(2954499865542011961/93770547200\) \(93770547200\) \([2]\) \(7680\) \(1.2009\) \(\Gamma_0(N)\)-optimal
4730.c4 4730b4 \([1, -1, 0, 54826, -10040732]\) \(18225478596775570119/53980968079601200\) \(-53980968079601200\) \([2]\) \(30720\) \(1.8940\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4730.c have rank \(1\).

Complex multiplication

The elliptic curves in class 4730.c do not have complex multiplication.

Modular form 4730.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.