Properties

 Label 272832fb Number of curves $6$ Conductor $272832$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("272832.fb1")

sage: E.isogeny_class()

Elliptic curves in class 272832fb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
272832.fb5 272832fb1 [0, 1, 0, -2458689, 1587952575] [2] 9437184 $$\Gamma_0(N)$$-optimal
272832.fb4 272832fb2 [0, 1, 0, -40106369, 97747656831] [2, 2] 18874368
272832.fb1 272832fb3 [0, 1, 0, -641700929, 6256511805375] [2] 37748736
272832.fb3 272832fb4 [0, 1, 0, -40874689, 93806943551] [2, 2] 37748736
272832.fb6 272832fb5 [0, 1, 0, 39140351, 416379575807] [2] 75497472
272832.fb2 272832fb6 [0, 1, 0, -133182849, -480959045505] [2] 75497472

Rank

sage: E.rank()

The elliptic curves in class 272832fb have rank $$0$$.

Modular form 272832.2.a.fb

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{13} - 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.