# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.o1 62400fe2 $$[0, -1, 0, -215233, 38511457]$$ $$-168256703745625/30371328$$ $$-199041535180800$$ $$[]$$ $$373248$$ $$1.7474$$
62400.o2 62400fe1 $$[0, -1, 0, 767, 175777]$$ $$7604375/2047032$$ $$-13415428915200$$ $$[]$$ $$124416$$ $$1.1981$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.o

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + q^{13} + 5q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 