# Properties

 Label 7800g Number of curves $4$ Conductor $7800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 7800g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.o4 7800g1 $$[0, 1, 0, -508, 15488]$$ $$-3631696/24375$$ $$-97500000000$$ $$$$ $$9216$$ $$0.79195$$ $$\Gamma_0(N)$$-optimal
7800.o3 7800g2 $$[0, 1, 0, -13008, 565488]$$ $$15214885924/38025$$ $$608400000000$$ $$[2, 2]$$ $$18432$$ $$1.1385$$
7800.o2 7800g3 $$[0, 1, 0, -18008, 85488]$$ $$20183398562/11567205$$ $$370150560000000$$ $$$$ $$36864$$ $$1.4851$$
7800.o1 7800g4 $$[0, 1, 0, -208008, 36445488]$$ $$31103978031362/195$$ $$6240000000$$ $$$$ $$36864$$ $$1.4851$$

## Rank

sage: E.rank()

The elliptic curves in class 7800g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7800g do not have complex multiplication.

## Modular form7800.2.a.g

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 