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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 18975.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18975.v1 | 18975p2 | \([1, 0, 1, -30951, -2082077]\) | \(209849322390625/1882056627\) | \(29407134796875\) | \([2]\) | \(46080\) | \(1.4072\) | |
18975.v2 | 18975p1 | \([1, 0, 1, -576, -77327]\) | \(-1349232625/164333367\) | \(-2567708859375\) | \([2]\) | \(23040\) | \(1.0606\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18975.v have rank \(1\).
Complex multiplication
The elliptic curves in class 18975.v do not have complex multiplication.Modular form 18975.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.