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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 24048g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24048.f2 | 24048g1 | \([0, 0, 0, -7275, -295526]\) | \(-14260515625/4382748\) | \(-13086815404032\) | \([2]\) | \(36864\) | \(1.2305\) | \(\Gamma_0(N)\)-optimal |
24048.f1 | 24048g2 | \([0, 0, 0, -123915, -16788422]\) | \(70470585447625/4518018\) | \(13490729459712\) | \([2]\) | \(73728\) | \(1.5771\) |
Rank
sage: E.rank()
The elliptic curves in class 24048g have rank \(0\).
Complex multiplication
The elliptic curves in class 24048g do not have complex multiplication.Modular form 24048.2.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 Cremona 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 Cremona labels.