# Properties

 Label 2100.a Number of curves 4 Conductor 2100 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2100.a1")

sage: E.isogeny_class()

## Elliptic curves in class 2100.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2100.a1 2100c4 [0, -1, 0, -45708, -3746088]  5184
2100.a2 2100c3 [0, -1, 0, -2833, -58838]  2592
2100.a3 2100c2 [0, -1, 0, -708, -2088]  1728
2100.a4 2100c1 [0, -1, 0, 167, -338]  864 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2100.a have rank $$0$$.

## Modular form2100.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - 6q^{11} - 2q^{13} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 