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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 15606.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15606.c1 | 15606f3 | \([1, -1, 0, -35601, -3419299]\) | \(-1167051/512\) | \(-2189259743049216\) | \([]\) | \(93312\) | \(1.6507\) | |
15606.c2 | 15606f1 | \([1, -1, 0, -921, 11131]\) | \(-132651/2\) | \(-1303428726\) | \([]\) | \(10368\) | \(0.55210\) | \(\Gamma_0(N)\)-optimal |
15606.c3 | 15606f2 | \([1, -1, 0, 3414, 53036]\) | \(9261/8\) | \(-3800798165016\) | \([]\) | \(31104\) | \(1.1014\) |
Rank
sage: E.rank()
The elliptic curves in class 15606.c have rank \(1\).
Complex multiplication
The elliptic curves in class 15606.c do not have complex multiplication.Modular form 15606.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.