# Properties

 Label 62400hv Number of curves $2$ Conductor $62400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hv1")

sage: E.isogeny_class()

## Elliptic curves in class 62400hv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.hr2 62400hv1 $$[0, 1, 0, -19833, 1067463]$$ $$107850176/117$$ $$936000000000$$ $$[2]$$ $$143360$$ $$1.2127$$ $$\Gamma_0(N)$$-optimal
62400.hr1 62400hv2 $$[0, 1, 0, -24833, 482463]$$ $$26463592/13689$$ $$876096000000000$$ $$[2]$$ $$286720$$ $$1.5592$$

## Rank

sage: E.rank()

The elliptic curves in class 62400hv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 62400hv do not have complex multiplication.

## Modular form 62400.2.a.hv

sage: E.q_eigenform(10)

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

## 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.