# Properties

 Label 12600.ci Number of curves $4$ Conductor $12600$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ci1")

sage: E.isogeny_class()

## Elliptic curves in class 12600.ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12600.ci1 12600cc3 [0, 0, 0, -67275, -6716250]  32768
12600.ci2 12600cc4 [0, 0, 0, -13275, 465750]  32768
12600.ci3 12600cc2 [0, 0, 0, -4275, -101250] [2, 2] 16384
12600.ci4 12600cc1 [0, 0, 0, 225, -6750]  8192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 12600.ci have rank $$0$$.

## Complex multiplication

The elliptic curves in class 12600.ci do not have complex multiplication.

## Modular form 12600.2.a.ci

sage: E.q_eigenform(10)

$$q + q^{7} + 4q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 