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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7220c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7220.f3 | 7220c1 | \([0, -1, 0, -481, -2634]\) | \(16384/5\) | \(3763670480\) | \([2]\) | \(3456\) | \(0.54227\) | \(\Gamma_0(N)\)-optimal |
| 7220.f4 | 7220c2 | \([0, -1, 0, 1324, -19240]\) | \(21296/25\) | \(-301093638400\) | \([2]\) | \(6912\) | \(0.88884\) | |
| 7220.f1 | 7220c3 | \([0, -1, 0, -14921, 706370]\) | \(488095744/125\) | \(94091762000\) | \([2]\) | \(10368\) | \(1.0916\) | |
| 7220.f2 | 7220c4 | \([0, -1, 0, -13116, 881816]\) | \(-20720464/15625\) | \(-188183524000000\) | \([2]\) | \(20736\) | \(1.4381\) |
Rank
sage: E.rank()
The elliptic curves in class 7220c have rank \(1\).
Complex multiplication
The elliptic curves in class 7220c do not have complex multiplication.Modular form 7220.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
