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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 74025.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74025.j1 | 74025ba4 | \([1, -1, 1, -3089480, -1895755728]\) | \(286307147687521969/29274322430115\) | \(333452828930528671875\) | \([2]\) | \(2654208\) | \(2.6737\) | |
| 74025.j2 | 74025ba2 | \([1, -1, 1, -710105, 198094272]\) | \(3476508505743169/526270448025\) | \(5994549322034765625\) | \([2, 2]\) | \(1327104\) | \(2.3271\) | |
| 74025.j3 | 74025ba1 | \([1, -1, 1, -681980, 216938022]\) | \(3079572809565169/90680625\) | \(1032908994140625\) | \([2]\) | \(663552\) | \(1.9805\) | \(\Gamma_0(N)\)-optimal |
| 74025.j4 | 74025ba3 | \([1, -1, 1, 1219270, 1085606772]\) | \(17598520411747631/54906731775315\) | \(-625421991628197421875\) | \([2]\) | \(2654208\) | \(2.6737\) |
Rank
sage: E.rank()
The elliptic curves in class 74025.j have rank \(2\).
Complex multiplication
The elliptic curves in class 74025.j do not have complex multiplication.Modular form 74025.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
