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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 360555.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360555.l1 | 360555l7 | \([1, 1, 0, -240370038, 1434294351993]\) | \(242970740812818720001/24375\) | \(154083224319375\) | \([2]\) | \(30965760\) | \(3.0700\) | |
| 360555.l2 | 360555l5 | \([1, 1, 0, -15023163, 22406041368]\) | \(59319456301170001/594140625\) | \(3755778592784765625\) | \([2, 2]\) | \(15482880\) | \(2.7234\) | |
| 360555.l3 | 360555l8 | \([1, 1, 0, -14662608, 23533064187]\) | \(-55150149867714721/5950927734375\) | \(-37617974687347412109375\) | \([2]\) | \(30965760\) | \(3.0700\) | |
| 360555.l4 | 360555l3 | \([1, 1, 0, -961518, 332071047]\) | \(15551989015681/1445900625\) | \(9140062783401005625\) | \([2, 2]\) | \(7741440\) | \(2.3769\) | |
| 360555.l5 | 360555l2 | \([1, 1, 0, -212673, -32017392]\) | \(168288035761/27720225\) | \(175229606024966025\) | \([2, 2]\) | \(3870720\) | \(2.0303\) | |
| 360555.l6 | 360555l1 | \([1, 1, 0, -203428, -35399213]\) | \(147281603041/5265\) | \(33281976452985\) | \([2]\) | \(1935360\) | \(1.6837\) | \(\Gamma_0(N)\)-optimal |
| 360555.l7 | 360555l4 | \([1, 1, 0, 388252, -179484387]\) | \(1023887723039/2798036865\) | \(-17687406848150801385\) | \([2]\) | \(7741440\) | \(2.3769\) | |
| 360555.l8 | 360555l6 | \([1, 1, 0, 1118607, 1574737722]\) | \(24487529386319/183539412225\) | \(-1160219258474293874025\) | \([2]\) | \(15482880\) | \(2.7234\) |
Rank
sage: E.rank()
The elliptic curves in class 360555.l have rank \(1\).
Complex multiplication
The elliptic curves in class 360555.l do not have complex multiplication.Modular form 360555.2.a.l
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
