# Properties

 Label 6720.g Number of curves $4$ Conductor $6720$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6720.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.g1 6720a3 $$[0, -1, 0, -56481, -5147775]$$ $$608119035935048/826875$$ $$27095040000$$ $$$$ $$12288$$ $$1.2761$$
6720.g2 6720a4 $$[0, -1, 0, -8961, 221121]$$ $$2428799546888/778248135$$ $$25501634887680$$ $$$$ $$12288$$ $$1.2761$$
6720.g3 6720a2 $$[0, -1, 0, -3561, -78039]$$ $$1219555693504/43758225$$ $$179233689600$$ $$[2, 2]$$ $$6144$$ $$0.92955$$
6720.g4 6720a1 $$[0, -1, 0, 84, -4410]$$ $$1012048064/130203045$$ $$-8332994880$$ $$$$ $$3072$$ $$0.58297$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6720.g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 6720.g do not have complex multiplication.

## Modular form6720.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 2q^{13} + q^{15} - 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 