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Properties

Label 1470.c
Number of curves $2$
Conductor $1470$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1470.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.c1 1470c1 \([1, 1, 0, -1068, -8112]\) \(393349474783/153600000\) \(52684800000\) \([2]\) \(2240\) \(0.75601\) \(\Gamma_0(N)\)-optimal
1470.c2 1470c2 \([1, 1, 0, 3412, -53808]\) \(12801408679457/11250000000\) \(-3858750000000\) \([2]\) \(4480\) \(1.1026\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1470.c have rank \(0\).

Complex multiplication

The elliptic curves in class 1470.c do not have complex multiplication.

Modular form 1470.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.