# Properties

 Label 12600.ck Number of curves $6$ Conductor $12600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("12600.ck1")

sage: E.isogeny_class()

## Elliptic curves in class 12600.ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12600.ck1 12600cb5 [0, 0, 0, -2358075, 1393717750] [2] 196608
12600.ck2 12600cb3 [0, 0, 0, -153075, 20002750] [2, 2] 98304
12600.ck3 12600cb2 [0, 0, 0, -40575, -2834750] [2, 2] 49152
12600.ck4 12600cb1 [0, 0, 0, -39450, -3015875] [2] 24576 $$\Gamma_0(N)$$-optimal
12600.ck5 12600cb4 [0, 0, 0, 53925, -14080250] [2] 98304
12600.ck6 12600cb6 [0, 0, 0, 251925, 107887750] [2] 196608

## Rank

sage: E.rank()

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

## Modular form 12600.2.a.ck

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.