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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 369600.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.eb1 | 369600eb3 | \([0, -1, 0, -3285633, 2293423137]\) | \(957681397954009/31185\) | \(127733760000000\) | \([2]\) | \(4718592\) | \(2.2080\) | |
| 369600.eb2 | 369600eb4 | \([0, -1, 0, -325633, -10656863]\) | \(932288503609/527295615\) | \(2159802839040000000\) | \([2]\) | \(4718592\) | \(2.2080\) | |
| 369600.eb3 | 369600eb2 | \([0, -1, 0, -205633, 35783137]\) | \(234770924809/1334025\) | \(5464166400000000\) | \([2, 2]\) | \(2359296\) | \(1.8615\) | |
| 369600.eb4 | 369600eb1 | \([0, -1, 0, -5633, 1183137]\) | \(-4826809/144375\) | \(-591360000000000\) | \([2]\) | \(1179648\) | \(1.5149\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.eb do not have complex multiplication.Modular form 369600.2.a.eb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
