# Properties

 Label 100905g Number of curves 4 Conductor 100905 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100905.s1")

sage: E.isogeny_class()

## Elliptic curves in class 100905g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100905.s3 100905g1 [1, 1, 0, -2422, -44489] [2] 120960 $$\Gamma_0(N)$$-optimal
100905.s2 100905g2 [1, 1, 0, -7227, 179424] [2, 2] 241920
100905.s4 100905g3 [1, 1, 0, 16798, 1145229] [2] 483840
100905.s1 100905g4 [1, 1, 0, -108132, 13640151] [2] 483840

## Rank

sage: E.rank()

The elliptic curves in class 100905g have rank $$0$$.

## Modular form 100905.2.a.s

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.