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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5265.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5265.g1 | 5265m2 | \([0, 0, 1, -2538, -48931]\) | \(30618648576/203125\) | \(11994328125\) | \([]\) | \(3888\) | \(0.76921\) | |
5265.g2 | 5265m1 | \([0, 0, 1, -198, 1028]\) | \(1177583616/54925\) | \(40040325\) | \([3]\) | \(1296\) | \(0.21990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5265.g have rank \(1\).
Complex multiplication
The elliptic curves in class 5265.g do not have complex multiplication.Modular form 5265.2.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.