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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 91200dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.ja3 | 91200dh1 | \([0, 1, 0, -12833, 38463]\) | \(57066625/32832\) | \(134479872000000\) | \([2]\) | \(331776\) | \(1.4006\) | \(\Gamma_0(N)\)-optimal |
| 91200.ja4 | 91200dh2 | \([0, 1, 0, 51167, 358463]\) | \(3616805375/2105352\) | \(-8623521792000000\) | \([2]\) | \(663552\) | \(1.7472\) | |
| 91200.ja1 | 91200dh3 | \([0, 1, 0, -684833, -218361537]\) | \(8671983378625/82308\) | \(337133568000000\) | \([2]\) | \(995328\) | \(1.9499\) | |
| 91200.ja2 | 91200dh4 | \([0, 1, 0, -668833, -229033537]\) | \(-8078253774625/846825858\) | \(-3468598714368000000\) | \([2]\) | \(1990656\) | \(2.2965\) |
Rank
sage: E.rank()
The elliptic curves in class 91200dh have rank \(0\).
Complex multiplication
The elliptic curves in class 91200dh do not have complex multiplication.Modular form 91200.2.a.dh
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.
