# Properties

 Label 7056.bq Number of curves $4$ Conductor $7056$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bq1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bq1 7056w3 $$[0, 0, 0, -1778259, -912726430]$$ $$7080974546692/189$$ $$16598831993856$$ $$$$ $$73728$$ $$2.0504$$
7056.bq2 7056w4 $$[0, 0, 0, -173019, 3322298]$$ $$6522128932/3720087$$ $$326714810135067648$$ $$$$ $$73728$$ $$2.0504$$
7056.bq3 7056w2 $$[0, 0, 0, -111279, -14224210]$$ $$6940769488/35721$$ $$784294811709696$$ $$[2, 2]$$ $$36864$$ $$1.7039$$
7056.bq4 7056w1 $$[0, 0, 0, -3234, -459277]$$ $$-2725888/64827$$ $$-88959365217072$$ $$$$ $$18432$$ $$1.3573$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7056.bq have rank $$1$$.

## Complex multiplication

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

## Modular form7056.2.a.bq

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 