# Properties

 Label 78400ig Number of curves $2$ Conductor $78400$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 78400ig

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.kh2 78400ig1 $$[0, -1, 0, 194367, 36039137]$$ $$19652/25$$ $$-1033052339200000000$$ $$[2]$$ $$1032192$$ $$2.1426$$ $$\Gamma_0(N)$$-optimal
78400.kh1 78400ig2 $$[0, -1, 0, -1177633, 350227137]$$ $$2185454/625$$ $$51652616960000000000$$ $$[2]$$ $$2064384$$ $$2.4891$$

## Rank

sage: E.rank()

The elliptic curves in class 78400ig have rank $$1$$.

## Complex multiplication

The elliptic curves in class 78400ig do not have complex multiplication.

## Modular form 78400.2.a.ig

sage: E.q_eigenform(10)

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

## 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.