# Properties

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

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 $$[0, 0, 0, -7248, 237508]$$ $$-225637236736/1715$$ $$-320060160$$ $$$$ $$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 form1260.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} - 3 q^{11} - q^{13} + 3 q^{17} + 2 q^{19} + O(q^{20})$$ ## 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. 