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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 39984.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39984.m1 | 39984i4 | \([0, -1, 0, -107424, -13513632]\) | \(569001644066/122451\) | \(29503974807552\) | \([2]\) | \(147456\) | \(1.5794\) | |
| 39984.m2 | 39984i3 | \([0, -1, 0, -48624, 4022880]\) | \(52767497666/1753941\) | \(422603580844032\) | \([4]\) | \(147456\) | \(1.5794\) | |
| 39984.m3 | 39984i2 | \([0, -1, 0, -7464, -158976]\) | \(381775972/127449\) | \(15354109338624\) | \([2, 2]\) | \(73728\) | \(1.2328\) | |
| 39984.m4 | 39984i1 | \([0, -1, 0, 1356, -17856]\) | \(9148592/9639\) | \(-290308790016\) | \([2]\) | \(36864\) | \(0.88623\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39984.m have rank \(1\).
Complex multiplication
The elliptic curves in class 39984.m do not have complex multiplication.Modular form 39984.2.a.m
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.
