# Properties

 Label 62400.q Number of curves $2$ Conductor $62400$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.q1 62400fs2 $$[0, -1, 0, -582273, 157776417]$$ $$666276475992821/58199166792$$ $$1907070297440256000$$ $$$$ $$1179648$$ $$2.2482$$
62400.q2 62400fs1 $$[0, -1, 0, -569473, 165597217]$$ $$623295446073461/5458752$$ $$178872385536000$$ $$$$ $$589824$$ $$1.9017$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.q

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. 