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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 213160.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 213160.c1 | 213160g4 | \([0, 0, 0, -570203, -165721242]\) | \(132304644/5\) | \(774831238599680\) | \([2]\) | \(1566720\) | \(1.9430\) | |
| 213160.c2 | 213160g2 | \([0, 0, 0, -37303, -2334102]\) | \(148176/25\) | \(968539048249600\) | \([2, 2]\) | \(783360\) | \(1.5964\) | |
| 213160.c3 | 213160g1 | \([0, 0, 0, -10658, 389017]\) | \(55296/5\) | \(12106738103120\) | \([2]\) | \(391680\) | \(1.2499\) | \(\Gamma_0(N)\)-optimal |
| 213160.c4 | 213160g3 | \([0, 0, 0, 69277, -13226578]\) | \(237276/625\) | \(-96853904824960000\) | \([2]\) | \(1566720\) | \(1.9430\) |
Rank
sage: E.rank()
The elliptic curves in class 213160.c have rank \(1\).
Complex multiplication
The elliptic curves in class 213160.c do not have complex multiplication.Modular form 213160.2.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 LMFDB 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 LMFDB labels.
