# Properties

 Label 6720.h Number of curves $6$ Conductor $6720$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 6720.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.h1 6720bh5 $$[0, -1, 0, -97601, 11765985]$$ $$784478485879202/221484375$$ $$29030400000000$$ $$[2]$$ $$32768$$ $$1.5643$$
6720.h2 6720bh3 $$[0, -1, 0, -6881, 135681]$$ $$549871953124/200930625$$ $$13168189440000$$ $$[2, 2]$$ $$16384$$ $$1.2177$$
6720.h3 6720bh2 $$[0, -1, 0, -2961, -59535]$$ $$175293437776/4862025$$ $$79659417600$$ $$[2, 2]$$ $$8192$$ $$0.87118$$
6720.h4 6720bh1 $$[0, -1, 0, -2941, -60419]$$ $$2748251600896/2205$$ $$2257920$$ $$[2]$$ $$4096$$ $$0.52460$$ $$\Gamma_0(N)$$-optimal
6720.h5 6720bh4 $$[0, -1, 0, 639, -198495]$$ $$439608956/259416045$$ $$-17001089925120$$ $$[2]$$ $$16384$$ $$1.2177$$
6720.h6 6720bh6 $$[0, -1, 0, 21119, 936481]$$ $$7947184069438/7533176175$$ $$-987388467609600$$ $$[2]$$ $$32768$$ $$1.5643$$

## Rank

sage: E.rank()

The elliptic curves in class 6720.h have rank $$0$$.

## Complex multiplication

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

## Modular form6720.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.