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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 229320cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.cv4 | 229320cu1 | \([0, 0, 0, -8967, 1160026]\) | \(-3631696/24375\) | \(-535180595040000\) | \([2]\) | \(884736\) | \(1.5095\) | \(\Gamma_0(N)\)-optimal |
| 229320.cv3 | 229320cu2 | \([0, 0, 0, -229467, 42217126]\) | \(15214885924/38025\) | \(3339526913049600\) | \([2, 2]\) | \(1769472\) | \(1.8561\) | |
| 229320.cv1 | 229320cu3 | \([0, 0, 0, -3669267, 2705310286]\) | \(31103978031362/195\) | \(34251558082560\) | \([2]\) | \(3538944\) | \(2.2026\) | |
| 229320.cv2 | 229320cu4 | \([0, 0, 0, -317667, 6778366]\) | \(20183398562/11567205\) | \(2031768173899376640\) | \([2]\) | \(3538944\) | \(2.2026\) |
Rank
sage: E.rank()
The elliptic curves in class 229320cu have rank \(0\).
Complex multiplication
The elliptic curves in class 229320cu do not have complex multiplication.Modular form 229320.2.a.cu
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.
