# Properties

 Label 95139j Number of curves 4 Conductor 95139 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("95139.c1")

sage: E.isogeny_class()

## Elliptic curves in class 95139j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95139.c3 95139j1 [1, -1, 1, -56399, -5097850] [2] 345600 $$\Gamma_0(N)$$-optimal
95139.c2 95139j2 [1, -1, 1, -99644, 3827918] [2, 2] 691200
95139.c4 95139j3 [1, -1, 1, 376051, 29515448] [2] 1382400
95139.c1 95139j4 [1, -1, 1, -1267259, 548870600] [2] 1382400

## Rank

sage: E.rank()

The elliptic curves in class 95139j have rank $$0$$.

## Modular form 95139.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{5} + 4q^{7} + 3q^{8} - 2q^{10} + q^{11} + 2q^{13} - 4q^{14} - q^{16} - 2q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.