# Properties

 Label 250096bl Number of curves $4$ Conductor $250096$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 250096bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250096.bl4 250096bl1 $$[0, 0, 0, 458101, 136022138]$$ $$22062729659823/29354283343$$ $$-14145544523860406272$$ $$[2]$$ $$4128768$$ $$2.3605$$ $$\Gamma_0(N)$$-optimal
250096.bl3 250096bl2 $$[0, 0, 0, -2838619, 1331412810]$$ $$5249244962308257/1448621666569$$ $$698076735283922046976$$ $$[2, 2]$$ $$8257536$$ $$2.7071$$
250096.bl1 250096bl3 $$[0, 0, 0, -41830859, 104122755898]$$ $$16798320881842096017/2132227789307$$ $$1027499897586398179328$$ $$[4]$$ $$16515072$$ $$3.0536$$
250096.bl2 250096bl4 $$[0, 0, 0, -16593899, -24954927270]$$ $$1048626554636928177/48569076788309$$ $$23404967178517567655936$$ $$[2]$$ $$16515072$$ $$3.0536$$

## Rank

sage: E.rank()

The elliptic curves in class 250096bl have rank $$1$$.

## Complex multiplication

The elliptic curves in class 250096bl do not have complex multiplication.

## Modular form 250096.2.a.bl

sage: E.q_eigenform(10)

$$q + 2q^{5} - 3q^{9} + q^{11} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$

## 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 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.