# Properties

 Label 435344.ba Number of curves $2$ Conductor $435344$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 435344.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.ba1 435344ba2 $$[0, 0, 0, -56615, -435006]$$ $$16241202000/9332687$$ $$11532056987080448$$ $$[2]$$ $$1935360$$ $$1.7716$$
435344.ba2 435344ba1 $$[0, 0, 0, -37180, 2748447]$$ $$73598976000/336973$$ $$26024068946512$$ $$[2]$$ $$967680$$ $$1.4250$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 435344.ba1.

## Rank

sage: E.rank()

The elliptic curves in class 435344.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 435344.ba do not have complex multiplication.

## Modular form 435344.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{7} - 3q^{9} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.