Properties

 Label 158400cc Number of curves 4 Conductor 158400 CM no Rank 2 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("158400.bc1")

sage: E.isogeny_class()

Elliptic curves in class 158400cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.bc4 158400cc1 [0, 0, 0, -40800, 3107000] [2] 663552 $$\Gamma_0(N)$$-optimal
158400.bc3 158400cc2 [0, 0, 0, -90300, -5902000] [2] 1327104
158400.bc2 158400cc3 [0, 0, 0, -400800, -96433000] [2] 1990656
158400.bc1 158400cc4 [0, 0, 0, -6390300, -6217702000] [2] 3981312

Rank

sage: E.rank()

The elliptic curves in class 158400cc have rank $$2$$.

Modular form 158400.2.a.bc

sage: E.q_eigenform(10)

$$q - 4q^{7} + q^{11} - 4q^{13} - 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.