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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 92736.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.r1 | 92736w2 | \([0, 0, 0, -6431724, -6278259024]\) | \(-5702623460245179/252448\) | \(-1302576230301696\) | \([]\) | \(3041280\) | \(2.3824\) | |
| 92736.r2 | 92736w1 | \([0, 0, 0, -72684, -10129744]\) | \(-5999796014211/2790817792\) | \(-19753095760183296\) | \([]\) | \(1013760\) | \(1.8330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92736.r have rank \(1\).
Complex multiplication
The elliptic curves in class 92736.r do not have complex multiplication.Modular form 92736.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
