# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 79560.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.bj1 79560bo4 $$[0, 0, 0, -294267, 61440694]$$ $$1887517194957938/21849165$$ $$32620628551680$$ $$$$ $$393216$$ $$1.7442$$
79560.bj2 79560bo2 $$[0, 0, 0, -18867, 907774]$$ $$994958062276/98903025$$ $$73830712550400$$ $$[2, 2]$$ $$196608$$ $$1.3976$$
79560.bj3 79560bo1 $$[0, 0, 0, -4287, -92414]$$ $$46689225424/7249905$$ $$1353006270720$$ $$$$ $$98304$$ $$1.0510$$ $$\Gamma_0(N)$$-optimal
79560.bj4 79560bo3 $$[0, 0, 0, 23253, 4386886]$$ $$931329171502/6107473125$$ $$-9118408515840000$$ $$$$ $$393216$$ $$1.7442$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 79560.2.a.bj

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{11} - q^{13} - q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 