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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 20280p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20280.c2 | 20280p1 | \([0, -1, 0, 121624, -17309124]\) | \(40254822716/49359375\) | \(-243966234096000000\) | \([2]\) | \(161280\) | \(2.0224\) | \(\Gamma_0(N)\)-optimal |
| 20280.c1 | 20280p2 | \([0, -1, 0, -723376, -165691124]\) | \(4234737878642/1247410125\) | \(12331029336148224000\) | \([2]\) | \(322560\) | \(2.3690\) |
Rank
sage: E.rank()
The elliptic curves in class 20280p have rank \(0\).
Complex multiplication
The elliptic curves in class 20280p do not have complex multiplication.Modular form 20280.2.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 Cremona 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 Cremona labels.
