# Properties

 Label 7056.cd Number of curves $2$ Conductor $7056$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cd1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.cd1 7056cb2 $$[0, 0, 0, -16023, 778610]$$ $$20720464/63$$ $$1383235999488$$ $$[2]$$ $$18432$$ $$1.1983$$
7056.cd2 7056cb1 $$[0, 0, 0, -588, 22295]$$ $$-16384/147$$ $$-201721916592$$ $$[2]$$ $$9216$$ $$0.85170$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.cd

sage: E.q_eigenform(10)

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

## 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.