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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 71148n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71148.r4 | 71148n1 | \([0, -1, 0, 39527, -1044602]\) | \(2048000/1323\) | \(-4411884941723952\) | \([2]\) | \(311040\) | \(1.6908\) | \(\Gamma_0(N)\)-optimal |
| 71148.r3 | 71148n2 | \([0, -1, 0, -167988, -8432136]\) | \(9826000/5103\) | \(272276327832106752\) | \([2]\) | \(622080\) | \(2.0374\) | |
| 71148.r2 | 71148n3 | \([0, -1, 0, -671953, -218117150]\) | \(-10061824000/352947\) | \(-1176992860564356528\) | \([2]\) | \(933120\) | \(2.2401\) | |
| 71148.r1 | 71148n4 | \([0, -1, 0, -10840188, -13733735112]\) | \(2640279346000/3087\) | \(164710371157694208\) | \([2]\) | \(1866240\) | \(2.5867\) |
Rank
sage: E.rank()
The elliptic curves in class 71148n have rank \(0\).
Complex multiplication
The elliptic curves in class 71148n do not have complex multiplication.Modular form 71148.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
