# Properties

 Label 62400.id Number of curves $4$ Conductor $62400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("id1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.id

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.id1 62400hm4 $$[0, 1, 0, -832033, -292395937]$$ $$31103978031362/195$$ $$399360000000$$ $$$$ $$589824$$ $$1.8317$$
62400.id2 62400hm3 $$[0, 1, 0, -72033, -755937]$$ $$20183398562/11567205$$ $$23689635840000000$$ $$$$ $$589824$$ $$1.8317$$
62400.id3 62400hm2 $$[0, 1, 0, -52033, -4575937]$$ $$15214885924/38025$$ $$38937600000000$$ $$[2, 2]$$ $$294912$$ $$1.4851$$
62400.id4 62400hm1 $$[0, 1, 0, -2033, -125937]$$ $$-3631696/24375$$ $$-6240000000000$$ $$$$ $$147456$$ $$1.1385$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.id

sage: E.q_eigenform(10)

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