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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 139650.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139650.ev1 | 139650dv3 | \([1, 1, 1, -15366409213, 733167005984531]\) | \(218289391029690300712901881/306514992000\) | \(563455973340750000000\) | \([2]\) | \(123863040\) | \(4.1466\) | |
| 139650.ev2 | 139650dv4 | \([1, 1, 1, -1005097213, 10330599776531]\) | \(61085713691774408830201/10268551781250000000\) | \(18876325758004394531250000000\) | \([2]\) | \(123863040\) | \(4.1466\) | |
| 139650.ev3 | 139650dv2 | \([1, 1, 1, -960409213, 11455217984531]\) | \(53294746224000958661881/1997017344000000\) | \(3671048336004000000000000\) | \([2, 2]\) | \(61931520\) | \(3.8000\) | |
| 139650.ev4 | 139650dv1 | \([1, 1, 1, -57241213, 196325696531]\) | \(-11283450590382195961/2530373271552000\) | \(-4651498203512832000000000\) | \([2]\) | \(30965760\) | \(3.4535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 139650.ev do not have complex multiplication.Modular form 139650.2.a.ev
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.
