# Properties

 Label 6760.i Number of curves $4$ Conductor $6760$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6760.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6760.i1 6760g3 $$[0, 0, 0, -18083, -935922]$$ $$132304644/5$$ $$24713262080$$ $$[2]$$ $$9216$$ $$1.0803$$
6760.i2 6760g2 $$[0, 0, 0, -1183, -13182]$$ $$148176/25$$ $$30891577600$$ $$[2, 2]$$ $$4608$$ $$0.73369$$
6760.i3 6760g1 $$[0, 0, 0, -338, 2197]$$ $$55296/5$$ $$386144720$$ $$[2]$$ $$2304$$ $$0.38711$$ $$\Gamma_0(N)$$-optimal
6760.i4 6760g4 $$[0, 0, 0, 2197, -74698]$$ $$237276/625$$ $$-3089157760000$$ $$[2]$$ $$9216$$ $$1.0803$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 6760.i do not have complex multiplication.

## 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.