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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 323400.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.cy1 | 323400cy2 | \([0, -1, 0, -15748683708, 760694941193412]\) | \(7343418009347613339536/136478763980097\) | \(8028295051747215976500000000\) | \([2]\) | \(387072000\) | \(4.4792\) | |
| 323400.cy2 | 323400cy1 | \([0, -1, 0, -952123083, 12699208478412]\) | \(-25963589461091772416/3923372657421063\) | \(-14424402180404082527718750000\) | \([2]\) | \(193536000\) | \(4.1327\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 323400.cy have rank \(1\).
Complex multiplication
The elliptic curves in class 323400.cy do not have complex multiplication.Modular form 323400.2.a.cy
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.
