# Properties

 Label 463680.ba Number of curves $2$ Conductor $463680$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 463680.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ba1 463680ba1 $$[0, 0, 0, -734508, -237686832]$$ $$8493409990827/185150000$$ $$955333332172800000$$ $$$$ $$5898240$$ $$2.2383$$ $$\Gamma_0(N)$$-optimal
463680.ba2 463680ba2 $$[0, 0, 0, 60372, -725107248]$$ $$4716275733/44023437500$$ $$-227151267840000000000$$ $$$$ $$11796480$$ $$2.5849$$

## Rank

sage: E.rank()

The elliptic curves in class 463680.ba have rank $$0$$.

## Complex multiplication

The elliptic curves in class 463680.ba do not have complex multiplication.

## Modular form 463680.2.a.ba

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 