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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 30576w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30576.cc3 | 30576w1 | \([0, 1, 0, -359, 1392]\) | \(2725888/1053\) | \(1982150352\) | \([2]\) | \(12288\) | \(0.48293\) | \(\Gamma_0(N)\)-optimal |
| 30576.cc2 | 30576w2 | \([0, 1, 0, -2564, -49764]\) | \(61918288/1521\) | \(45809697024\) | \([2, 2]\) | \(24576\) | \(0.82951\) | |
| 30576.cc4 | 30576w3 | \([0, 1, 0, 376, -154428]\) | \(48668/85683\) | \(-10322451729408\) | \([2]\) | \(49152\) | \(1.1761\) | |
| 30576.cc1 | 30576w4 | \([0, 1, 0, -40784, -3183804]\) | \(62275269892/39\) | \(4698430464\) | \([2]\) | \(49152\) | \(1.1761\) |
Rank
sage: E.rank()
The elliptic curves in class 30576w have rank \(1\).
Complex multiplication
The elliptic curves in class 30576w do not have complex multiplication.Modular form 30576.2.a.w
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 Cremona 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 Cremona labels.
