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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 23120x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23120.l1 | 23120x1 | \([0, -1, 0, -185056, -38252800]\) | \(-24529249/8000\) | \(-228581619826688000\) | \([]\) | \(176256\) | \(2.0434\) | \(\Gamma_0(N)\)-optimal |
| 23120.l2 | 23120x2 | \([0, -1, 0, 1387104, 347869696]\) | \(10329972191/7812500\) | \(-223224238112000000000\) | \([]\) | \(528768\) | \(2.5927\) |
Rank
sage: E.rank()
The elliptic curves in class 23120x have rank \(1\).
Complex multiplication
The elliptic curves in class 23120x do not have complex multiplication.Modular form 23120.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
