Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 382200l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 382200.l3 | 382200l1 | \([0, -1, 0, -113108, -14593788]\) | \(340062928/273\) | \(128472708000000\) | \([2]\) | \(1966080\) | \(1.6371\) | \(\Gamma_0(N)\)-optimal |
| 382200.l2 | 382200l2 | \([0, -1, 0, -137608, -7782788]\) | \(153091012/74529\) | \(140292197136000000\) | \([2, 2]\) | \(3932160\) | \(1.9837\) | |
| 382200.l1 | 382200l3 | \([0, -1, 0, -1166608, 479963212]\) | \(46640233586/599781\) | \(2258036315808000000\) | \([2]\) | \(7864320\) | \(2.3302\) | |
| 382200.l4 | 382200l4 | \([0, -1, 0, 499392, -60016788]\) | \(3658553134/2528253\) | \(-9518285990304000000\) | \([2]\) | \(7864320\) | \(2.3302\) |
Rank
sage: E.rank()
The elliptic curves in class 382200l have rank \(1\).
Complex multiplication
The elliptic curves in class 382200l do not have complex multiplication.Modular form 382200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
