# Properties

 Label 6960.l Number of curves $4$ Conductor $6960$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("l1")

E.isogeny_class()

## Elliptic curves in class 6960.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6960.l1 6960bf3 $$[0, -1, 0, -4120, 101680]$$ $$1888690601881/31827645$$ $$130366033920$$ $$[4]$$ $$12288$$ $$0.93080$$
6960.l2 6960bf2 $$[0, -1, 0, -520, -2000]$$ $$3803721481/1703025$$ $$6975590400$$ $$[2, 2]$$ $$6144$$ $$0.58422$$
6960.l3 6960bf1 $$[0, -1, 0, -440, -3408]$$ $$2305199161/1305$$ $$5345280$$ $$[2]$$ $$3072$$ $$0.23765$$ $$\Gamma_0(N)$$-optimal
6960.l4 6960bf4 $$[0, -1, 0, 1800, -16848]$$ $$157376536199/118918125$$ $$-487088640000$$ $$[2]$$ $$12288$$ $$0.93080$$

## Rank

sage: E.rank()

The elliptic curves in class 6960.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6960.l do not have complex multiplication.

## Modular form6960.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 4 q^{7} + q^{9} + 4 q^{11} + 6 q^{13} - q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.