# Properties

 Label 4368.ba Number of curves $2$ Conductor $4368$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 4368.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.ba1 4368i1 $$[0, 1, 0, -211, 1112]$$ $$65239066624/5733$$ $$91728$$ $$[2]$$ $$1792$$ $$-0.0067467$$ $$\Gamma_0(N)$$-optimal
4368.ba2 4368i2 $$[0, 1, 0, -196, 1292]$$ $$-3269383504/1217307$$ $$-311630592$$ $$[2]$$ $$3584$$ $$0.33983$$

## Rank

sage: E.rank()

The elliptic curves in class 4368.ba have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4368.ba do not have complex multiplication.

## Modular form4368.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{3} + 4 q^{5} - q^{7} + q^{9} - 6 q^{11} - q^{13} + 4 q^{15} + 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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 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.