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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1530.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1530.f1 | 1530e4 | \([1, -1, 0, -1674, 26730]\) | \(711882749089/1721250\) | \(1254791250\) | \([2]\) | \(1024\) | \(0.62468\) | |
| 1530.f2 | 1530e3 | \([1, -1, 0, -1494, -21762]\) | \(506071034209/2505630\) | \(1826604270\) | \([2]\) | \(1024\) | \(0.62468\) | |
| 1530.f3 | 1530e2 | \([1, -1, 0, -144, 108]\) | \(454756609/260100\) | \(189612900\) | \([2, 2]\) | \(512\) | \(0.27811\) | |
| 1530.f4 | 1530e1 | \([1, -1, 0, 36, 0]\) | \(6967871/4080\) | \(-2974320\) | \([2]\) | \(256\) | \(-0.068467\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1530.f have rank \(1\).
Complex multiplication
The elliptic curves in class 1530.f do not have complex multiplication.Modular form 1530.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
