Properties

 Label 138600f Number of curves $2$ Conductor $138600$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 138600f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138600.cx2 138600f1 $$[0, 0, 0, -33375, -2218750]$$ $$11279504/693$$ $$252598500000000$$ $$$$ $$368640$$ $$1.5154$$ $$\Gamma_0(N)$$-optimal
138600.cx1 138600f2 $$[0, 0, 0, -100875, 9593750]$$ $$77860436/17787$$ $$25933446000000000$$ $$$$ $$737280$$ $$1.8620$$

Rank

sage: E.rank()

The elliptic curves in class 138600f have rank $$1$$.

Complex multiplication

The elliptic curves in class 138600f do not have complex multiplication.

Modular form 138600.2.a.f

sage: E.q_eigenform(10)

$$q + q^{7} - q^{11} - 4 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$ 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. 