# Properties

 Label 2112.q Number of curves 4 Conductor 2112 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2112.q1")

sage: E.isogeny_class()

## Elliptic curves in class 2112.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.q1 2112n3 [0, 1, 0, -1254529, -541258849] [2] 15360
2112.q2 2112n2 [0, 1, 0, -78409, -8476489] [2, 2] 7680
2112.q3 2112n4 [0, 1, 0, -73569, -9563553] [4] 15360
2112.q4 2112n1 [0, 1, 0, -5204, -116478] [2] 3840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2112.q have rank $$0$$.

## Modular form2112.2.a.q

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} - 4q^{7} + q^{9} - q^{11} + 2q^{13} - 2q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.