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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 7098.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7098.ba1 | 7098w2 | \([1, 0, 0, -10098, -381564]\) | \(673822943613625/19421724672\) | \(3282271469568\) | \([]\) | \(18144\) | \(1.1797\) | |
7098.ba2 | 7098w1 | \([1, 0, 0, -1323, 18225]\) | \(1515434103625/17635968\) | \(2980478592\) | \([]\) | \(6048\) | \(0.63035\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7098.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 7098.ba do not have complex multiplication.Modular form 7098.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.