# Properties

 Label 6760.i Number of curves 4 Conductor 6760 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6760.i1")

sage: E.isogeny_class()

## Elliptic curves in class 6760.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6760.i1 6760g3 [0, 0, 0, -18083, -935922]  9216
6760.i2 6760g2 [0, 0, 0, -1183, -13182] [2, 2] 4608
6760.i3 6760g1 [0, 0, 0, -338, 2197]  2304 $$\Gamma_0(N)$$-optimal
6760.i4 6760g4 [0, 0, 0, 2197, -74698]  9216

## Rank

sage: E.rank()

The elliptic curves in class 6760.i have rank $$0$$.

## Modular form6760.2.a.i

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} - 3q^{9} - 4q^{11} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 