# Properties

 Label 70560.cn Number of curves $4$ Conductor $70560$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cn1")

sage: E.isogeny_class()

## Elliptic curves in class 70560.cn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70560.cn1 70560bv4 $$[0, 0, 0, -45008460147, -3675270815038186]$$ $$229625675762164624948320008/9568125$$ $$420157934844480000$$ $$[2]$$ $$82575360$$ $$4.2822$$
70560.cn2 70560bv3 $$[0, 0, 0, -2822675772, -57012396271936]$$ $$7079962908642659949376/100085966990454375$$ $$35160003196130573398955520000$$ $$[2]$$ $$82575360$$ $$4.2822$$
70560.cn3 70560bv1 $$[0, 0, 0, -2813028897, -57426100576936]$$ $$448487713888272974160064/91549016015625$$ $$502515455041730025000000$$ $$[2, 2]$$ $$41287680$$ $$3.9357$$ $$\Gamma_0(N)$$-optimal
70560.cn4 70560bv2 $$[0, 0, 0, -2803384227, -57839426767654]$$ $$-55486311952875723077768/801237030029296875$$ $$-35184123938392734375000000000$$ $$[2]$$ $$82575360$$ $$4.2822$$

## Rank

sage: E.rank()

The elliptic curves in class 70560.cn have rank $$0$$.

## Complex multiplication

The elliptic curves in class 70560.cn do not have complex multiplication.

## Modular form 70560.2.a.cn

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.