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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 2352.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2352.v1 | 2352v5 | \([0, 1, 0, -614672, -185691948]\) | \(53297461115137/147\) | \(70837874688\) | \([2]\) | \(12288\) | \(1.7403\) | |
| 2352.v2 | 2352v3 | \([0, 1, 0, -38432, -2908620]\) | \(13027640977/21609\) | \(10413167579136\) | \([2, 2]\) | \(6144\) | \(1.3937\) | |
| 2352.v3 | 2352v4 | \([0, 1, 0, -30592, 2036852]\) | \(6570725617/45927\) | \(22131775991808\) | \([4]\) | \(6144\) | \(1.3937\) | |
| 2352.v4 | 2352v6 | \([0, 1, 0, -26672, -4710252]\) | \(-4354703137/17294403\) | \(-8334005119168512\) | \([2]\) | \(12288\) | \(1.7403\) | |
| 2352.v5 | 2352v2 | \([0, 1, 0, -3152, -15660]\) | \(7189057/3969\) | \(1912622616576\) | \([2, 2]\) | \(3072\) | \(1.0472\) | |
| 2352.v6 | 2352v1 | \([0, 1, 0, 768, -1548]\) | \(103823/63\) | \(-30359089152\) | \([2]\) | \(1536\) | \(0.70059\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2352.v have rank \(0\).
Complex multiplication
The elliptic curves in class 2352.v do not have complex multiplication.Modular form 2352.2.a.v
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
