# Properties

 Label 100016.h Number of curves 4 Conductor 100016 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100016.h1")
sage: E.isogeny_class()

## Elliptic curves in class 100016.h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100016.h1 100016p4 [0, 0, 0, -97691, 7610314] 4 454656
100016.h2 100016p2 [0, 0, 0, -39931, -2982870] 4 227328
100016.h3 100016p1 [0, 0, 0, -39611, -3034390] 2 113664 $$\Gamma_0(N)$$-optimal
100016.h4 100016p3 [0, 0, 0, 12709, -10278774] 2 454656

## Rank

sage: E.rank()

The elliptic curves in class 100016.h have rank $$1$$.

## Modular form None

sage: E.q_eigenform(10)
$$q - 2q^{5} + q^{7} - 3q^{9} - 2q^{13} - 6q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.