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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2352.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2352.i1 | 2352c5 | \([0, -1, 0, -18832, -988448]\) | \(3065617154/9\) | \(2168506368\) | \([2]\) | \(3072\) | \(1.0208\) | |
| 2352.i2 | 2352c4 | \([0, -1, 0, -3152, 69168]\) | \(28756228/3\) | \(361417728\) | \([2]\) | \(1536\) | \(0.67418\) | |
| 2352.i3 | 2352c3 | \([0, -1, 0, -1192, -14720]\) | \(1556068/81\) | \(9758278656\) | \([2, 2]\) | \(1536\) | \(0.67418\) | |
| 2352.i4 | 2352c2 | \([0, -1, 0, -212, 960]\) | \(35152/9\) | \(271063296\) | \([2, 2]\) | \(768\) | \(0.32760\) | |
| 2352.i5 | 2352c1 | \([0, -1, 0, 33, 78]\) | \(2048/3\) | \(-5647152\) | \([2]\) | \(384\) | \(-0.018971\) | \(\Gamma_0(N)\)-optimal |
| 2352.i6 | 2352c6 | \([0, -1, 0, 768, -60192]\) | \(207646/6561\) | \(-1580841142272\) | \([2]\) | \(3072\) | \(1.0208\) |
Rank
sage: E.rank()
The elliptic curves in class 2352.i have rank \(0\).
Complex multiplication
The elliptic curves in class 2352.i do not have complex multiplication.Modular form 2352.2.a.i
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
