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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 422331bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422331.bl2 | 422331bl1 | \([1, 1, 0, 465, 4152]\) | \(42875/51\) | \(-13182217503\) | \([2]\) | \(221184\) | \(0.62808\) | \(\Gamma_0(N)\)-optimal* |
422331.bl1 | 422331bl2 | \([1, 1, 0, -2720, 36639]\) | \(8615125/2601\) | \(672293092653\) | \([2]\) | \(442368\) | \(0.97465\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422331bl have rank \(1\).
Complex multiplication
The elliptic curves in class 422331bl do not have complex multiplication.Modular form 422331.2.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 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.