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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 40950bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40950.cp3 | 40950bl1 | \([1, -1, 0, -12717, 539941]\) | \(19968681097/628992\) | \(7164612000000\) | \([2]\) | \(98304\) | \(1.2415\) | \(\Gamma_0(N)\)-optimal |
| 40950.cp2 | 40950bl2 | \([1, -1, 0, -30717, -1314059]\) | \(281397674377/96589584\) | \(1100215730250000\) | \([2, 2]\) | \(196608\) | \(1.5881\) | |
| 40950.cp4 | 40950bl3 | \([1, -1, 0, 90783, -9211559]\) | \(7264187703863/7406095788\) | \(-84360059835187500\) | \([2]\) | \(393216\) | \(1.9347\) | |
| 40950.cp1 | 40950bl4 | \([1, -1, 0, -440217, -112288559]\) | \(828279937799497/193444524\) | \(2203454031187500\) | \([2]\) | \(393216\) | \(1.9347\) |
Rank
sage: E.rank()
The elliptic curves in class 40950bl have rank \(1\).
Complex multiplication
The elliptic curves in class 40950bl do not have complex multiplication.Modular form 40950.2.a.bl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
