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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 270480.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270480.p1 | 270480p2 | \([0, -1, 0, -7195176, 1735835760]\) | \(85486955243540761/46777901234400\) | \(22541817046326991257600\) | \([2]\) | \(14745600\) | \(2.9799\) | |
| 270480.p2 | 270480p1 | \([0, -1, 0, -4310056, -3420450704]\) | \(18374873741826841/136564270080\) | \(65808997624389304320\) | \([2]\) | \(7372800\) | \(2.6333\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270480.p have rank \(0\).
Complex multiplication
The elliptic curves in class 270480.p do not have complex multiplication.Modular form 270480.2.a.p
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.
