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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 144900.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144900.bl1 | 144900c2 | \([0, 0, 0, -33375, 1543750]\) | \(11279504/3703\) | \(1349743500000000\) | \([2]\) | \(691200\) | \(1.6062\) | |
144900.bl2 | 144900c1 | \([0, 0, 0, 6000, 165625]\) | \(1048576/1127\) | \(-25674468750000\) | \([2]\) | \(345600\) | \(1.2597\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 144900.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 144900.bl do not have complex multiplication.Modular form 144900.2.a.bl
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.