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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5445l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5445.f2 | 5445l1 | \([0, 0, 1, -55902, 14278635]\) | \(-123633664/492075\) | \(-76895391202326675\) | \([]\) | \(38016\) | \(1.9255\) | \(\Gamma_0(N)\)-optimal |
5445.f1 | 5445l2 | \([0, 0, 1, -6524562, 6414694272]\) | \(-196566176333824/421875\) | \(-65925403980046875\) | \([3]\) | \(114048\) | \(2.4748\) |
Rank
sage: E.rank()
The elliptic curves in class 5445l have rank \(0\).
Complex multiplication
The elliptic curves in class 5445l do not have complex multiplication.Modular form 5445.2.a.l
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 Cremona 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 Cremona labels.