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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 67626.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67626.w1 | 67626bh3 | \([1, -1, 1, -1195214, 503239389]\) | \(-10730978619193/6656\) | \(-117120891603456\) | \([]\) | \(907200\) | \(2.0203\) | |
67626.w2 | 67626bh2 | \([1, -1, 1, -11759, 981087]\) | \(-10218313/17576\) | \(-309272354390376\) | \([]\) | \(302400\) | \(1.4710\) | |
67626.w3 | 67626bh1 | \([1, -1, 1, 1246, -28101]\) | \(12167/26\) | \(-457503482826\) | \([]\) | \(100800\) | \(0.92169\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67626.w have rank \(0\).
Complex multiplication
The elliptic curves in class 67626.w do not have complex multiplication.Modular form 67626.2.a.w
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.