Properties

 Label 207368j Number of curves $2$ Conductor $207368$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 207368j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
207368.ba2 207368j1 $$[0, -1, 0, -2186004, -816925276]$$ $$21296/7$$ $$379731626567481192704$$ $$$$ $$5935104$$ $$2.6518$$ $$\Gamma_0(N)$$-optimal
207368.ba1 207368j2 $$[0, -1, 0, -14109664, 19791928668]$$ $$1431644/49$$ $$10632485543889473395712$$ $$$$ $$11870208$$ $$2.9984$$

Rank

sage: E.rank()

The elliptic curves in class 207368j have rank $$0$$.

Complex multiplication

The elliptic curves in class 207368j do not have complex multiplication.

Modular form 207368.2.a.j

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 