Properties

Label 1260.c
Number of curves $2$
Conductor $1260$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1260.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1260.c1 1260g2 \([0, 0, 0, -7248, 237508]\) \(-225637236736/1715\) \(-320060160\) \([3]\) \(1080\) \(0.80685\)  
1260.c2 1260g1 \([0, 0, 0, -48, 628]\) \(-65536/875\) \(-163296000\) \([]\) \(360\) \(0.25755\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1260.c have rank \(0\).

Complex multiplication

The elliptic curves in class 1260.c do not have complex multiplication.

Modular form 1260.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 3 q^{11} - q^{13} + 3 q^{17} + 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.