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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 72450bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.x2 | 72450bj1 | \([1, -1, 0, -1842, -141184]\) | \(-60698457/725788\) | \(-8267178937500\) | \([2]\) | \(196608\) | \(1.1605\) | \(\Gamma_0(N)\)-optimal |
72450.x1 | 72450bj2 | \([1, -1, 0, -53592, -4746934]\) | \(1494447319737/5411854\) | \(61644399468750\) | \([2]\) | \(393216\) | \(1.5070\) |
Rank
sage: E.rank()
The elliptic curves in class 72450bj have rank \(1\).
Complex multiplication
The elliptic curves in class 72450bj do not have complex multiplication.Modular form 72450.2.a.bj
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.