# Properties

 Label 100800.v Number of curves 6 Conductor 100800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.v1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.v1 100800me6 [0, 0, 0, -11289900, -14601022000] [2] 2097152
100800.v2 100800me4 [0, 0, 0, -705900, -227950000] [2, 2] 1048576
100800.v3 100800me3 [0, 0, 0, -561900, 161138000] [2] 1048576
100800.v4 100800me5 [0, 0, 0, -489900, -370078000] [2] 2097152
100800.v5 100800me2 [0, 0, 0, -57900, -1150000] [2, 2] 524288
100800.v6 100800me1 [0, 0, 0, 14100, -142000] [2] 262144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 100800.v have rank $$1$$.

## Modular form 100800.2.a.v

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.