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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 35280.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.n1 | 35280br4 | \([0, 0, 0, -201243, -34709542]\) | \(10262905636/13125\) | \(1152696666240000\) | \([2]\) | \(196608\) | \(1.7980\) | |
| 35280.n2 | 35280br3 | \([0, 0, 0, -148323, 21819602]\) | \(4108974916/36015\) | \(3162999652162560\) | \([2]\) | \(196608\) | \(1.7980\) | |
| 35280.n3 | 35280br2 | \([0, 0, 0, -16023, -221578]\) | \(20720464/11025\) | \(242066299910400\) | \([2, 2]\) | \(98304\) | \(1.4514\) | |
| 35280.n4 | 35280br1 | \([0, 0, 0, 3822, -27097]\) | \(4499456/2835\) | \(-3890351248560\) | \([2]\) | \(49152\) | \(1.1048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.n have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.n do not have complex multiplication.Modular form 35280.2.a.n
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.
