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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 77280.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77280.v1 | 77280f4 | \([0, -1, 0, -52900800, -148077735000]\) | \(31977203346157644779097608/28589809959375\) | \(14637982699200000\) | \([2]\) | \(3440640\) | \(2.8334\) | |
| 77280.v2 | 77280f3 | \([0, -1, 0, -4084680, -1141918428]\) | \(14720683462954119927368/7416057586669921875\) | \(3797021484375000000000\) | \([4]\) | \(3440640\) | \(2.8334\) | |
| 77280.v3 | 77280f1 | \([0, -1, 0, -3307050, -2311785000]\) | \(62498004782515366780864/59053556337890625\) | \(3779427605625000000\) | \([2, 2]\) | \(1720320\) | \(2.4868\) | \(\Gamma_0(N)\)-optimal |
| 77280.v4 | 77280f2 | \([0, -1, 0, -2541425, -3411069375]\) | \(-443195996177646496576/971300939313403125\) | \(-3978448647427699200000\) | \([2]\) | \(3440640\) | \(2.8334\) |
Rank
sage: E.rank()
The elliptic curves in class 77280.v have rank \(1\).
Complex multiplication
The elliptic curves in class 77280.v do not have complex multiplication.Modular form 77280.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
