# Properties

 Label 94136f Number of curves $4$ Conductor $94136$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 94136f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94136.f4 94136f1 [0, 0, 0, 1681, 137842]  140800 $$\Gamma_0(N)$$-optimal
94136.f3 94136f2 [0, 0, 0, -31939, 2067630] [2, 2] 281600
94136.f2 94136f3 [0, 0, 0, -99179, -9511098]  563200
94136.f1 94136f4 [0, 0, 0, -502619, 137152790]  563200

## Rank

sage: E.rank()

The elliptic curves in class 94136f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 94136f do not have complex multiplication.

## Modular form 94136.2.a.f

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 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. 