# Properties

 Label 393008.ba Number of curves $4$ Conductor $393008$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 393008.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
393008.ba1 393008ba3 $$[0, 0, 0, -103296611, 404044863266]$$ $$16798320881842096017/2132227789307$$ $$15472114051696632737792$$ $$[2]$$ $$41287680$$ $$3.2796$$
393008.ba2 393008ba4 $$[0, 0, 0, -40976771, -96836758590]$$ $$1048626554636928177/48569076788309$$ $$352432464872134575509504$$ $$[2]$$ $$41287680$$ $$3.2796$$
393008.ba3 393008ba2 $$[0, 0, 0, -7009651, 5166502770]$$ $$5249244962308257/1448621666569$$ $$10511653471226446680064$$ $$[2, 2]$$ $$20643840$$ $$2.9330$$
393008.ba4 393008ba1 $$[0, 0, 0, 1131229, 527829346]$$ $$22062729659823/29354283343$$ $$-213003892954760900608$$ $$[2]$$ $$10321920$$ $$2.5865$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 393008.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 393008.ba do not have complex multiplication.

## Modular form 393008.2.a.ba

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{7} - 3q^{9} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.