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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 67600.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.k1 | 67600cg2 | \([0, 1, 0, -2215308, 1268374888]\) | \(-368484688\) | \(-3262922884000000\) | \([]\) | \(1010880\) | \(2.2106\) | |
67600.k2 | 67600cg1 | \([0, 1, 0, -18308, 2902888]\) | \(-208\) | \(-3262922884000000\) | \([]\) | \(336960\) | \(1.6613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67600.k have rank \(0\).
Complex multiplication
The elliptic curves in class 67600.k do not have complex multiplication.Modular form 67600.2.a.k
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.