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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 234.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 234.c1 | 234d3 | \([1, -1, 1, -186656, -30992493]\) | \(986551739719628473/111045168\) | \(80951927472\) | \([2]\) | \(1280\) | \(1.5174\) | |
| 234.c2 | 234d4 | \([1, -1, 1, -21056, 404115]\) | \(1416134368422073/725251155408\) | \(528708092292432\) | \([2]\) | \(1280\) | \(1.5174\) | |
| 234.c3 | 234d2 | \([1, -1, 1, -11696, -479469]\) | \(242702053576633/2554695936\) | \(1862373337344\) | \([2, 2]\) | \(640\) | \(1.1708\) | |
| 234.c4 | 234d1 | \([1, -1, 1, -176, -18669]\) | \(-822656953/207028224\) | \(-150923575296\) | \([4]\) | \(320\) | \(0.82424\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234.c have rank \(0\).
Complex multiplication
The elliptic curves in class 234.c do not have complex multiplication.Modular form 234.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
