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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 57960l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.d4 | 57960l1 | \([0, 0, 0, -833178, -292721623]\) | \(5483900709072173056/277725\) | \(3239384400\) | \([2]\) | \(327680\) | \(1.7464\) | \(\Gamma_0(N)\)-optimal |
| 57960.d3 | 57960l2 | \([0, 0, 0, -833223, -292688422]\) | \(342799332162880336/77131175625\) | \(14394528519840000\) | \([2, 2]\) | \(655360\) | \(2.0930\) | |
| 57960.d5 | 57960l3 | \([0, 0, 0, -738723, -361616722]\) | \(-59722927783102084/41113267272525\) | \(-30690889565870822400\) | \([2]\) | \(1310720\) | \(2.4395\) | |
| 57960.d2 | 57960l4 | \([0, 0, 0, -928443, -221635258]\) | \(118566490663726564/40187675390625\) | \(29999938928400000000\) | \([2, 2]\) | \(1310720\) | \(2.4395\) | |
| 57960.d6 | 57960l5 | \([0, 0, 0, 2723037, -1535437762]\) | \(1495639267637215678/1547698974609375\) | \(-2310702187500000000000\) | \([2]\) | \(2621440\) | \(2.7861\) | |
| 57960.d1 | 57960l6 | \([0, 0, 0, -6103443, 5639569742]\) | \(16841893263968213282/543703603314375\) | \(811745130119535360000\) | \([2]\) | \(2621440\) | \(2.7861\) |
Rank
sage: E.rank()
The elliptic curves in class 57960l have rank \(0\).
Complex multiplication
The elliptic curves in class 57960l do not have complex multiplication.Modular form 57960.2.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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
