# Properties

 Label 114240ha Number of curves $2$ Conductor $114240$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ha1")

sage: E.isogeny_class()

## Elliptic curves in class 114240ha

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114240.dr2 114240ha1 $$[0, -1, 0, 5215, -174783]$$ $$59822347031/83966400$$ $$-22011287961600$$ $$[2]$$ $$221184$$ $$1.2458$$ $$\Gamma_0(N)$$-optimal
114240.dr1 114240ha2 $$[0, -1, 0, -33185, -1703103]$$ $$15417797707369/4080067320$$ $$1069565167534080$$ $$[2]$$ $$442368$$ $$1.5924$$

## Rank

sage: E.rank()

The elliptic curves in class 114240ha have rank $$0$$.

## Complex multiplication

The elliptic curves in class 114240ha do not have complex multiplication.

## Modular form 114240.2.a.ha

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - q^{7} + q^{9} + 2q^{11} + 2q^{13} - q^{15} + q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.