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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 87120.ex
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.ex1 | 87120fm2 | \([0, 0, 0, -83127, -9149294]\) | \(192143824/1815\) | \(600067677116160\) | \([2]\) | \(368640\) | \(1.6564\) | |
| 87120.ex2 | 87120fm1 | \([0, 0, 0, -1452, -344729]\) | \(-16384/2475\) | \(-51142131572400\) | \([2]\) | \(184320\) | \(1.3099\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.ex have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.ex do not have complex multiplication.Modular form 87120.2.a.ex
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
