# Properties

 Label 7056.bt Number of curves $2$ Conductor $7056$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bt1 7056g2 $$[0, 0, 0, -5439, 154350]$$ $$21882096/7$$ $$5692329216$$ $$$$ $$6144$$ $$0.84666$$
7056.bt2 7056g1 $$[0, 0, 0, -294, 3087]$$ $$-55296/49$$ $$-2490394032$$ $$$$ $$3072$$ $$0.50008$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.bt

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 