# Properties

 Label 94192i Number of curves $4$ Conductor $94192$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 94192i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94192.r4 94192i1 [0, 0, 0, 841, -48778]  96768 $$\Gamma_0(N)$$-optimal
94192.r3 94192i2 [0, 0, 0, -15979, -731670] [2, 2] 193536
94192.r2 94192i3 [0, 0, 0, -49619, 3365682]  387072
94192.r1 94192i4 [0, 0, 0, -251459, -48534110]  387072

## Rank

sage: E.rank()

The elliptic curves in class 94192i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 94192i do not have complex multiplication.

## Modular form 94192.2.a.i

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. 