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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 72450.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.g1 | 72450ba2 | \([1, -1, 0, -136242, -18087084]\) | \(24553362849625/1755162752\) | \(19992400722000000\) | \([2]\) | \(774144\) | \(1.8748\) | |
72450.g2 | 72450ba1 | \([1, -1, 0, 7758, -1239084]\) | \(4533086375/60669952\) | \(-691068672000000\) | \([2]\) | \(387072\) | \(1.5282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72450.g have rank \(0\).
Complex multiplication
The elliptic curves in class 72450.g do not have complex multiplication.Modular form 72450.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.