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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 76608fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76608.bw4 | 76608fu1 | \([0, 0, 0, -156936, -9372904]\) | \(572616640141312/280535480757\) | \(209418614243177472\) | \([2]\) | \(786432\) | \(2.0169\) | \(\Gamma_0(N)\)-optimal |
| 76608.bw2 | 76608fu2 | \([0, 0, 0, -1337916, 589147760]\) | \(22174957026242512/278654127129\) | \(3328227060564639744\) | \([2, 2]\) | \(1572864\) | \(2.3635\) | |
| 76608.bw3 | 76608fu3 | \([0, 0, 0, -229836, 1535448080]\) | \(-28104147578308/21301741002339\) | \(-1017706524882051465216\) | \([2]\) | \(3145728\) | \(2.7100\) | |
| 76608.bw1 | 76608fu4 | \([0, 0, 0, -21341676, 37948169936]\) | \(22501000029889239268/3620708343\) | \(172982034893832192\) | \([2]\) | \(3145728\) | \(2.7100\) |
Rank
sage: E.rank()
The elliptic curves in class 76608fu have rank \(1\).
Complex multiplication
The elliptic curves in class 76608fu do not have complex multiplication.Modular form 76608.2.a.fu
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.
