# Properties

 Label 62400ig Number of curves $2$ Conductor $62400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ig1")

sage: E.isogeny_class()

## Elliptic curves in class 62400ig

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.ib2 62400ig1 $$[0, 1, 0, -793, -8857]$$ $$107850176/117$$ $$59904000$$ $$[2]$$ $$28672$$ $$0.40795$$ $$\Gamma_0(N)$$-optimal
62400.ib1 62400ig2 $$[0, 1, 0, -993, -4257]$$ $$26463592/13689$$ $$56070144000$$ $$[2]$$ $$57344$$ $$0.75452$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.ig

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} + 2q^{11} + q^{13} - 2q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.