# Properties

 Label 2100.j Number of curves $2$ Conductor $2100$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 2100.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2100.j1 2100q2 $$[0, 1, 0, -57748, -5358892]$$ $$665567485783184/257298363$$ $$8233547616000$$ $$$$ $$8064$$ $$1.4436$$
2100.j2 2100q1 $$[0, 1, 0, -3073, -110092]$$ $$-1605176213504/1640558367$$ $$-3281116734000$$ $$$$ $$4032$$ $$1.0971$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 2100.j do not have complex multiplication.

## Modular form2100.2.a.j

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - 4 q^{11} + 6 q^{13} - 2 q^{17} + 6 q^{19} + O(q^{20})$$

## 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. 