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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 361920d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.d3 | 361920d1 | \([0, -1, 0, -822461, 287364525]\) | \(60085575315625916416/435688632405\) | \(446145159582720\) | \([2]\) | \(3932160\) | \(1.9885\) | \(\Gamma_0(N)\)-optimal |
| 361920.d2 | 361920d2 | \([0, -1, 0, -839281, 275015281]\) | \(3990492186049586896/319127676581025\) | \(5228587853103513600\) | \([2, 2]\) | \(7864320\) | \(2.3351\) | |
| 361920.d4 | 361920d3 | \([0, -1, 0, 851999, 1242089185]\) | \(1043663576155667996/10778351982913125\) | \(-706370075552194560000\) | \([2]\) | \(15728640\) | \(2.6816\) | |
| 361920.d1 | 361920d4 | \([0, -1, 0, -2799681, -1482679359]\) | \(37031353559394592324/6920935791466905\) | \(453570448029575086080\) | \([2]\) | \(15728640\) | \(2.6816\) |
Rank
sage: E.rank()
The elliptic curves in class 361920d have rank \(1\).
Complex multiplication
The elliptic curves in class 361920d do not have complex multiplication.Modular form 361920.2.a.d
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.
