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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 20280.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20280.b1 | 20280d4 | \([0, -1, 0, -1406136, 642253260]\) | \(31103978031362/195\) | \(1927634442240\) | \([2]\) | \(258048\) | \(1.9629\) | |
| 20280.b2 | 20280d3 | \([0, -1, 0, -121736, 1648620]\) | \(20183398562/11567205\) | \(114345347479234560\) | \([2]\) | \(258048\) | \(1.9629\) | |
| 20280.b3 | 20280d2 | \([0, -1, 0, -87936, 10044540]\) | \(15214885924/38025\) | \(187944358118400\) | \([2, 2]\) | \(129024\) | \(1.6163\) | |
| 20280.b4 | 20280d1 | \([0, -1, 0, -3436, 276340]\) | \(-3631696/24375\) | \(-30119288160000\) | \([2]\) | \(64512\) | \(1.2697\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20280.b have rank \(1\).
Complex multiplication
The elliptic curves in class 20280.b do not have complex multiplication.Modular form 20280.2.a.b
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.
