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SageMath
sage: E = EllipticCurve("e1")
sage: E.isogeny_class()
Elliptic curves in class 9576.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.e1 | 9576g3 | \([0, 0, 0, -29091, 1584830]\) | \(1823652903746/328593657\) | \(490587701151744\) | \([2]\) | \(40960\) | \(1.5379\) | |
| 9576.e2 | 9576g2 | \([0, 0, 0, -8571, -282490]\) | \(93280467172/7800849\) | \(5823302575104\) | \([2, 2]\) | \(20480\) | \(1.1913\) | |
| 9576.e3 | 9576g1 | \([0, 0, 0, -8391, -295846]\) | \(350104249168/2793\) | \(521240832\) | \([2]\) | \(10240\) | \(0.84476\) | \(\Gamma_0(N)\)-optimal |
| 9576.e4 | 9576g4 | \([0, 0, 0, 9069, -1295026]\) | \(55251546334/517244049\) | \(-772241227204608\) | \([2]\) | \(40960\) | \(1.5379\) |
Rank
sage: E.rank()
The elliptic curves in class 9576.e have rank \(0\).
Complex multiplication
The elliptic curves in class 9576.e do not have complex multiplication.Modular form 9576.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
