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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 16900.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16900.c1 | 16900m1 | \([0, 1, 0, -1188633, 498393988]\) | \(153910165504/845\) | \(1019663401250000\) | \([2]\) | \(193536\) | \(2.0732\) | \(\Gamma_0(N)\)-optimal |
| 16900.c2 | 16900m2 | \([0, 1, 0, -1167508, 516983988]\) | \(-9115564624/714025\) | \(-13785849184900000000\) | \([2]\) | \(387072\) | \(2.4198\) |
Rank
sage: E.rank()
The elliptic curves in class 16900.c have rank \(0\).
Complex multiplication
The elliptic curves in class 16900.c do not have complex multiplication.Modular form 16900.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
