# Properties

 Label 100010h Number of curves 2 Conductor 100010 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100010.i1")

sage: E.isogeny_class()

## Elliptic curves in class 100010h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100010.i2 100010h1 [1, 1, 1, -275, -1583] [2] 54144 $$\Gamma_0(N)$$-optimal
100010.i1 100010h2 [1, 1, 1, -1275, 15617] [2] 108288

## Rank

sage: E.rank()

The elliptic curves in class 100010h have rank $$0$$.

## Modular form 100010.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + q^{5} + 2q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + 2q^{11} + 2q^{12} + 2q^{13} - 4q^{14} + 2q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.