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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 146205.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
146205.g1 | 146205h2 | \([0, 0, 1, -38988, 2824193]\) | \(2359296/125\) | \(347251528396125\) | \([]\) | \(517104\) | \(1.5469\) | |
146205.g2 | 146205h1 | \([0, 0, 1, -6498, -200626]\) | \(884736/5\) | \(171482236245\) | \([]\) | \(172368\) | \(0.99758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146205.g have rank \(0\).
Complex multiplication
The elliptic curves in class 146205.g do not have complex multiplication.Modular form 146205.2.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.