# Properties

 Label 100800.c Number of curves 2 Conductor 100800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.c1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.c1 100800cd2 [0, 0, 0, -2335500, 1372950000]  2211840
100800.c2 100800cd1 [0, 0, 0, -175500, 12150000]  1105920 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 100800.c have rank $$0$$.

## Modular form 100800.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 