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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 29400eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.dh4 | 29400eb1 | \([0, 1, 0, 4492, 55488]\) | \(21296/15\) | \(-7058940000000\) | \([2]\) | \(55296\) | \(1.1539\) | \(\Gamma_0(N)\)-optimal |
| 29400.dh3 | 29400eb2 | \([0, 1, 0, -20008, 447488]\) | \(470596/225\) | \(423536400000000\) | \([2, 2]\) | \(110592\) | \(1.5005\) | |
| 29400.dh2 | 29400eb3 | \([0, 1, 0, -167008, -26012512]\) | \(136835858/1875\) | \(7058940000000000\) | \([2]\) | \(221184\) | \(1.8471\) | |
| 29400.dh1 | 29400eb4 | \([0, 1, 0, -265008, 52387488]\) | \(546718898/405\) | \(1524731040000000\) | \([2]\) | \(221184\) | \(1.8471\) |
Rank
sage: E.rank()
The elliptic curves in class 29400eb have rank \(0\).
Complex multiplication
The elliptic curves in class 29400eb do not have complex multiplication.Modular form 29400.2.a.eb
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.
