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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 179088cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179088.i4 | 179088cd1 | \([0, -1, 0, 636, -2592]\) | \(110961434288/73773063\) | \(-18885904128\) | \([2]\) | \(122880\) | \(0.66057\) | \(\Gamma_0(N)\)-optimal |
179088.i3 | 179088cd2 | \([0, -1, 0, -2744, -18816]\) | \(2232206341348/1127549241\) | \(1154610422784\) | \([2, 2]\) | \(245760\) | \(1.0071\) | |
179088.i2 | 179088cd3 | \([0, -1, 0, -24064, 1430944]\) | \(752515177946114/8396328213\) | \(17195680180224\) | \([2]\) | \(491520\) | \(1.3537\) | |
179088.i1 | 179088cd4 | \([0, -1, 0, -35504, -2560992]\) | \(2416784053495394/2314298259\) | \(4739682834432\) | \([2]\) | \(491520\) | \(1.3537\) |
Rank
sage: E.rank()
The elliptic curves in class 179088cd have rank \(1\).
Complex multiplication
The elliptic curves in class 179088cd do not have complex multiplication.Modular form 179088.2.a.cd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.