# Properties

 Label 62400.h Number of curves $2$ Conductor $62400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.h1 62400by2 $$[0, -1, 0, -14556833, -19692938463]$$ $$666276475992821/58199166792$$ $$29797973397504000000000$$ $$[2]$$ $$5898240$$ $$3.0529$$
62400.h2 62400by1 $$[0, -1, 0, -14236833, -20671178463]$$ $$623295446073461/5458752$$ $$2794881024000000000$$ $$[2]$$ $$2949120$$ $$2.7064$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 62400.h have rank $$1$$.

## Complex multiplication

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

## Modular form 62400.2.a.h

sage: E.q_eigenform(10)

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

## 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 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.