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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 348480.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.i1 | 348480i4 | \([0, 0, 0, -6779388, 3690660688]\) | \(1628514404944/664335375\) | \(14056945377052317696000\) | \([2]\) | \(26542080\) | \(2.9474\) | |
| 348480.i2 | 348480i2 | \([0, 0, 0, -3120348, -2121358448]\) | \(158792223184/16335\) | \(345638982018908160\) | \([2]\) | \(8847360\) | \(2.3981\) | |
| 348480.i3 | 348480i1 | \([0, 0, 0, -180048, -38449928]\) | \(-488095744/200475\) | \(-265120810071321600\) | \([2]\) | \(4423680\) | \(2.0516\) | \(\Gamma_0(N)\)-optimal |
| 348480.i4 | 348480i3 | \([0, 0, 0, 1388112, 420393688]\) | \(223673040896/187171875\) | \(-247527916810416000000\) | \([2]\) | \(13271040\) | \(2.6009\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.i have rank \(0\).
Complex multiplication
The elliptic curves in class 348480.i do not have complex multiplication.Modular form 348480.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
