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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 303240.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303240.c1 | 303240c4 | \([0, -1, 0, -1045576, -411118820]\) | \(2624033547076/324135\) | \(15615197837245440\) | \([2]\) | \(4644864\) | \(2.1305\) | |
| 303240.c2 | 303240c2 | \([0, -1, 0, -70876, -5253740]\) | \(3269383504/893025\) | \(10755365857286400\) | \([2, 2]\) | \(2322432\) | \(1.7839\) | |
| 303240.c3 | 303240c1 | \([0, -1, 0, -25751, 1533060]\) | \(2508888064/118125\) | \(88916715090000\) | \([2]\) | \(1161216\) | \(1.4374\) | \(\Gamma_0(N)\)-optimal |
| 303240.c4 | 303240c3 | \([0, -1, 0, 181824, -34465860]\) | \(13799183324/18600435\) | \(-896075623995632640\) | \([2]\) | \(4644864\) | \(2.1305\) |
Rank
sage: E.rank()
The elliptic curves in class 303240.c have rank \(0\).
Complex multiplication
The elliptic curves in class 303240.c do not have complex multiplication.Modular form 303240.2.a.c
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.
