# Properties

 Label 62400.gt Number of curves $2$ Conductor $62400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("gt1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.gt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.gt1 62400gk2 $$[0, 1, 0, -73633, 6864863]$$ $$10779215329/1232010$$ $$5046312960000000$$ $$$$ $$442368$$ $$1.7454$$
62400.gt2 62400gk1 $$[0, 1, 0, 6367, 544863]$$ $$6967871/35100$$ $$-143769600000000$$ $$$$ $$221184$$ $$1.3988$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.gt

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} + 4q^{11} - q^{13} - 8q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 