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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 61347.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61347.v1 | 61347i2 | \([1, 1, 0, -9077, 1847058]\) | \(-276301129/4782969\) | \(-1431991307238921\) | \([]\) | \(235200\) | \(1.5893\) | |
61347.v2 | 61347i1 | \([1, 1, 0, -1212, -16947]\) | \(-658489/9\) | \(-2694544281\) | \([]\) | \(33600\) | \(0.61636\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61347.v have rank \(0\).
Complex multiplication
The elliptic curves in class 61347.v do not have complex multiplication.Modular form 61347.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.