# Properties

 Label 79560.b Number of curves $4$ Conductor $79560$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 79560.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.b1 79560bm4 $$[0, 0, 0, -812163, 210014638]$$ $$79364416584061444/20404090514925$$ $$15231571953029452800$$ $$$$ $$1572864$$ $$2.3902$$
79560.b2 79560bm2 $$[0, 0, 0, -285663, -56078462]$$ $$13813960087661776/714574355625$$ $$133356724544160000$$ $$[2, 2]$$ $$786432$$ $$2.0436$$
79560.b3 79560bm1 $$[0, 0, 0, -282018, -57645083]$$ $$212670222886967296/616241925$$ $$7187845813200$$ $$$$ $$393216$$ $$1.6970$$ $$\Gamma_0(N)$$-optimal
79560.b4 79560bm3 $$[0, 0, 0, 182517, -221907818]$$ $$900753985478876/29018422265625$$ $$-21662136147600000000$$ $$$$ $$1572864$$ $$2.3902$$

## Rank

sage: E.rank()

The elliptic curves in class 79560.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 79560.b do not have complex multiplication.

## Modular form 79560.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} + q^{13} - q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 