# Properties

 Label 57960bp Number of curves $4$ Conductor $57960$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bp1")

sage: E.isogeny_class()

## Elliptic curves in class 57960bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57960.w4 57960bp1 $$[0, 0, 0, -9183, 21922]$$ $$458891455696/264449745$$ $$49352669210880$$ $$$$ $$122880$$ $$1.3171$$ $$\Gamma_0(N)$$-optimal
57960.w2 57960bp2 $$[0, 0, 0, -104403, 12952798]$$ $$168591300897604/472410225$$ $$352652343321600$$ $$[2, 2]$$ $$245760$$ $$1.6636$$
57960.w3 57960bp3 $$[0, 0, 0, -63003, 23327638]$$ $$-18524646126002/146738831715$$ $$-219079901839841280$$ $$$$ $$491520$$ $$2.0102$$
57960.w1 57960bp4 $$[0, 0, 0, -1669323, 830154022]$$ $$344577854816148242/2716875$$ $$4056272640000$$ $$$$ $$491520$$ $$2.0102$$

## Rank

sage: E.rank()

The elliptic curves in class 57960bp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 57960bp do not have complex multiplication.

## Modular form 57960.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 4 q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 