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SageMath
E = EllipticCurve("rz1")
E.isogeny_class()
Elliptic curves in class 369600.rz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.rz1 | 369600rz1 | \([0, 1, 0, -3008, -62262]\) | \(3010936384/121275\) | \(121275000000\) | \([2]\) | \(540672\) | \(0.89295\) | \(\Gamma_0(N)\)-optimal |
| 369600.rz2 | 369600rz2 | \([0, 1, 0, 1367, -224137]\) | \(4410944/343035\) | \(-21954240000000\) | \([2]\) | \(1081344\) | \(1.2395\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.rz have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.rz do not have complex multiplication.Modular form 369600.2.a.rz
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
