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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 40560.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.cg1 | 40560t4 | \([0, 1, 0, -1406136, -642253260]\) | \(31103978031362/195\) | \(1927634442240\) | \([2]\) | \(516096\) | \(1.9629\) | |
| 40560.cg2 | 40560t3 | \([0, 1, 0, -121736, -1648620]\) | \(20183398562/11567205\) | \(114345347479234560\) | \([2]\) | \(516096\) | \(1.9629\) | |
| 40560.cg3 | 40560t2 | \([0, 1, 0, -87936, -10044540]\) | \(15214885924/38025\) | \(187944358118400\) | \([2, 2]\) | \(258048\) | \(1.6163\) | |
| 40560.cg4 | 40560t1 | \([0, 1, 0, -3436, -276340]\) | \(-3631696/24375\) | \(-30119288160000\) | \([2]\) | \(129024\) | \(1.2697\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40560.cg have rank \(0\).
Complex multiplication
The elliptic curves in class 40560.cg do not have complex multiplication.Modular form 40560.2.a.cg
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.
