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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 97461.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97461.j1 | 97461b1 | \([1, -1, 1, -20642852, 36100109350]\) | \(420100556152674123/62939003491\) | \(145746923103770267097\) | \([2]\) | \(6635520\) | \(2.8823\) | \(\Gamma_0(N)\)-optimal |
97461.j2 | 97461b2 | \([1, -1, 1, -18731117, 43055001280]\) | \(-313859434290315003/164114213839849\) | \(-380036867094225826804683\) | \([2]\) | \(13271040\) | \(3.2289\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.j have rank \(1\).
Complex multiplication
The elliptic curves in class 97461.j do not have complex multiplication.Modular form 97461.2.a.j
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.