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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 90972i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90972.g4 | 90972i1 | \([0, 0, 0, 21660, -418399]\) | \(2048000/1323\) | \(-725987195366832\) | \([2]\) | \(331776\) | \(1.5405\) | \(\Gamma_0(N)\)-optimal |
| 90972.g3 | 90972i2 | \([0, 0, 0, -92055, -3443218]\) | \(9826000/5103\) | \(44803781199781632\) | \([2]\) | \(663552\) | \(1.8870\) | |
| 90972.g2 | 90972i3 | \([0, 0, 0, -368220, -88570267]\) | \(-10061824000/352947\) | \(-193677250675084848\) | \([2]\) | \(995328\) | \(2.0898\) | |
| 90972.g1 | 90972i4 | \([0, 0, 0, -5940255, -5572567114]\) | \(2640279346000/3087\) | \(27103521960361728\) | \([2]\) | \(1990656\) | \(2.4363\) |
Rank
sage: E.rank()
The elliptic curves in class 90972i have rank \(1\).
Complex multiplication
The elliptic curves in class 90972i do not have complex multiplication.Modular form 90972.2.a.i
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.
