Properties

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

Show commands: SageMath
sage: E = EllipticCurve("df1")

sage: E.isogeny_class()

Elliptic curves in class 138600df

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138600.ba2 138600df1 $$[0, 0, 0, -1335, -17750]$$ $$11279504/693$$ $$16166304000$$ $$$$ $$73728$$ $$0.71072$$ $$\Gamma_0(N)$$-optimal
138600.ba1 138600df2 $$[0, 0, 0, -4035, 76750]$$ $$77860436/17787$$ $$1659740544000$$ $$$$ $$147456$$ $$1.0573$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 138600.2.a.df

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. 