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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 72450.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.v1 | 72450x2 | \([1, -1, 0, -165942, 87966]\) | \(44365623586201/25674468750\) | \(292448245605468750\) | \([2]\) | \(884736\) | \(2.0409\) | |
72450.v2 | 72450x1 | \([1, -1, 0, -114192, 14836716]\) | \(14457238157881/49990500\) | \(569423039062500\) | \([2]\) | \(442368\) | \(1.6943\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72450.v have rank \(0\).
Complex multiplication
The elliptic curves in class 72450.v do not have complex multiplication.Modular form 72450.2.a.v
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.