# Properties

 Label 2070.c Number of curves $2$ Conductor $2070$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 2070.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.c1 2070e2 $$[1, -1, 0, -35325, 2564325]$$ $$6687281588245201/165600$$ $$120722400$$ $$[2]$$ $$3840$$ $$1.0692$$
2070.c2 2070e1 $$[1, -1, 0, -2205, 40581]$$ $$-1626794704081/8125440$$ $$-5923445760$$ $$[2]$$ $$1920$$ $$0.72264$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2070.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2070.c do not have complex multiplication.

## Modular form2070.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 2q^{11} + 4q^{13} + q^{16} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.