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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5445.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5445.g1 | 5445k2 | \([0, 0, 1, -53922, -4819455]\) | \(-196566176333824/421875\) | \(-37213171875\) | \([]\) | \(10368\) | \(1.2758\) | |
5445.g2 | 5445k1 | \([0, 0, 1, -462, -10728]\) | \(-123633664/492075\) | \(-43405443675\) | \([]\) | \(3456\) | \(0.72653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5445.g have rank \(0\).
Complex multiplication
The elliptic curves in class 5445.g do not have complex multiplication.Modular form 5445.2.a.g
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.