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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 60112.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60112.r1 | 60112x3 | \([0, 1, 0, -2124824, 1191447188]\) | \(-10730978619193/6656\) | \(-658061964345344\) | \([]\) | \(725760\) | \(2.1641\) | |
| 60112.r2 | 60112x2 | \([0, 1, 0, -20904, 2311604]\) | \(-10218313/17576\) | \(-1737694874599424\) | \([]\) | \(241920\) | \(1.6148\) | |
| 60112.r3 | 60112x1 | \([0, 1, 0, 2216, -65132]\) | \(12167/26\) | \(-2570554548224\) | \([]\) | \(80640\) | \(1.0655\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60112.r have rank \(1\).
Complex multiplication
The elliptic curves in class 60112.r do not have complex multiplication.Modular form 60112.2.a.r
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.
