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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 115600cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115600.a2 | 115600cf1 | \([0, 0, 0, -16090075, -36561317750]\) | \(-60698457/40960\) | \(-310871002964295680000000\) | \([]\) | \(24440832\) | \(3.2084\) | \(\Gamma_0(N)\)-optimal |
| 115600.a1 | 115600cf2 | \([0, 0, 0, -14578222075, 677524878510250]\) | \(-45145776875761017/2441406250\) | \(-18529355702656250000000000000\) | \([]\) | \(317730816\) | \(4.4909\) |
Rank
sage: E.rank()
The elliptic curves in class 115600cf have rank \(0\).
Complex multiplication
The elliptic curves in class 115600cf do not have complex multiplication.Modular form 115600.2.a.cf
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
