Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 84270.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84270.h1 | 84270l4 | \([1, 0, 1, -2916135319, 33976652846726]\) | \(123734700956222105895361/49105035004573786500\) | \(1088381729093559570712944958500\) | \([2]\) | \(207028224\) | \(4.4618\) | |
| 84270.h2 | 84270l2 | \([1, 0, 1, -2543942819, 49370683523726]\) | \(82146777284059539615361/30229559822250000\) | \(670018880671058049320250000\) | \([2, 2]\) | \(103514112\) | \(4.1153\) | |
| 84270.h3 | 84270l1 | \([1, 0, 1, -2543718099, 49379844639022]\) | \(82125009821717833875841/11127456000\) | \(246632953231057824000\) | \([2]\) | \(51757056\) | \(3.7687\) | \(\Gamma_0(N)\)-optimal |
| 84270.h4 | 84270l3 | \([1, 0, 1, -2175345839, 64178403720662]\) | \(-51363360304251682409281/50556099454101562500\) | \(-1120543645574346791493164062500\) | \([2]\) | \(207028224\) | \(4.4618\) |
Rank
sage: E.rank()
The elliptic curves in class 84270.h have rank \(0\).
Complex multiplication
The elliptic curves in class 84270.h do not have complex multiplication.Modular form 84270.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
