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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 42350.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42350.da1 | 42350cp4 | \([1, 1, 1, -10648063, 13296357031]\) | \(4823468134087681/30382271150\) | \(841000729074455468750\) | \([2]\) | \(3317760\) | \(2.8525\) | |
| 42350.da2 | 42350cp2 | \([1, 1, 1, -816813, -272280469]\) | \(2177286259681/105875000\) | \(2930687826171875000\) | \([2]\) | \(1105920\) | \(2.3032\) | |
| 42350.da3 | 42350cp3 | \([1, 1, 1, -272313, 451178531]\) | \(-80677568161/3131816380\) | \(-86690683718268437500\) | \([2]\) | \(1658880\) | \(2.5059\) | |
| 42350.da4 | 42350cp1 | \([1, 1, 1, 30187, -16486469]\) | \(109902239/4312000\) | \(-119358922375000000\) | \([2]\) | \(552960\) | \(1.9566\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42350.da have rank \(0\).
Complex multiplication
The elliptic curves in class 42350.da do not have complex multiplication.Modular form 42350.2.a.da
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
