# Properties

 Label 7056.x Number of curves $4$ Conductor $7056$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.x1 7056br4 $$[0, 0, 0, -806295, 278668978]$$ $$2640279346000/3087$$ $$67778563974912$$ $$$$ $$55296$$ $$1.9371$$
7056.x2 7056br3 $$[0, 0, 0, -49980, 4429159]$$ $$-10061824000/352947$$ $$-484334321737392$$ $$$$ $$27648$$ $$1.5905$$
7056.x3 7056br2 $$[0, 0, 0, -12495, 172186]$$ $$9826000/5103$$ $$112042115958528$$ $$$$ $$18432$$ $$1.3878$$
7056.x4 7056br1 $$[0, 0, 0, 2940, 20923]$$ $$2048000/1323$$ $$-1815497249328$$ $$$$ $$9216$$ $$1.0412$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7056.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7056.x do not have complex multiplication.

## Modular form7056.2.a.x

sage: E.q_eigenform(10)

$$q - 6q^{11} - 2q^{13} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 