# Properties

 Label 6422.h Number of curves $3$ Conductor $6422$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6422.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6422.h1 6422f3 $$[1, 0, 0, -14453, -5380831]$$ $$-69173457625/2550136832$$ $$-12309023411929088$$ $$[]$$ $$36936$$ $$1.7676$$
6422.h2 6422f1 $$[1, 0, 0, -2623, 51505]$$ $$-413493625/152$$ $$-733674968$$ $$[]$$ $$4104$$ $$0.66903$$ $$\Gamma_0(N)$$-optimal
6422.h3 6422f2 $$[1, 0, 0, 1602, 196676]$$ $$94196375/3511808$$ $$-16950826460672$$ $$[]$$ $$12312$$ $$1.2183$$

## Rank

sage: E.rank()

The elliptic curves in class 6422.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6422.h do not have complex multiplication.

## Modular form6422.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} + 6q^{11} + q^{12} + q^{14} + q^{16} + 3q^{17} - 2q^{18} - q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.