# Properties

 Label 13950.cm Number of curves $6$ Conductor $13950$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("13950.cm1")

sage: E.isogeny_class()

## Elliptic curves in class 13950.cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13950.cm1 13950cf5 [1, -1, 1, -69192005, 221547010497] [4] 786432
13950.cm2 13950cf4 [1, -1, 1, -4324505, 3462475497] [2, 2] 393216
13950.cm3 13950cf6 [1, -1, 1, -4257005, 3575740497] [2] 786432
13950.cm4 13950cf3 [1, -1, 1, -832505, -227740503] [2] 393216
13950.cm5 13950cf2 [1, -1, 1, -274505, 52375497] [2, 2] 196608
13950.cm6 13950cf1 [1, -1, 1, 13495, 3415497] [2] 98304 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 13950.cm have rank $$1$$.

## Modular form 13950.2.a.cm

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + 4q^{11} - 6q^{13} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.