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SageMath
E = EllipticCurve("df1")
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 | \([0, 0, 0, -1335, -17750]\) | \(11279504/693\) | \(16166304000\) | \([2]\) | \(73728\) | \(0.71072\) | \(\Gamma_0(N)\)-optimal |
138600.ba1 | 138600df2 | \([0, 0, 0, -4035, 76750]\) | \(77860436/17787\) | \(1659740544000\) | \([2]\) | \(147456\) | \(1.0573\) |
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)
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.