# Properties

 Label 62400.m Number of curves $4$ Conductor $62400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.m1 62400ff4 $$[0, -1, 0, -22752033, -41750856063]$$ $$2543984126301795848/909361981125$$ $$465593334336000000000$$ $$[2]$$ $$4718592$$ $$2.9351$$
62400.m2 62400ff3 $$[0, -1, 0, -11752033, 15191643937]$$ $$350584567631475848/8259273550125$$ $$4228748057664000000000$$ $$[4]$$ $$4718592$$ $$2.9351$$
62400.m3 62400ff2 $$[0, -1, 0, -1627033, -451481063]$$ $$7442744143086784/2927948765625$$ $$187388721000000000000$$ $$[2, 2]$$ $$2359296$$ $$2.5885$$
62400.m4 62400ff1 $$[0, -1, 0, 326092, -51090438]$$ $$3834800837445824/3342041015625$$ $$-3342041015625000000$$ $$[2]$$ $$1179648$$ $$2.2419$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.m

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.