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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 6720bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6720.by3 | 6720bb1 | \([0, 1, 0, -1265, -17745]\) | \(13674725584/945\) | \(15482880\) | \([2]\) | \(3072\) | \(0.43333\) | \(\Gamma_0(N)\)-optimal |
6720.by2 | 6720bb2 | \([0, 1, 0, -1345, -15457]\) | \(4108974916/893025\) | \(58525286400\) | \([2, 2]\) | \(6144\) | \(0.77990\) | |
6720.by1 | 6720bb3 | \([0, 1, 0, -6945, 207423]\) | \(282678688658/18600435\) | \(2437996216320\) | \([4]\) | \(12288\) | \(1.1265\) | |
6720.by4 | 6720bb4 | \([0, 1, 0, 2975, -90625]\) | \(22208984782/40516875\) | \(-5310627840000\) | \([2]\) | \(12288\) | \(1.1265\) |
Rank
sage: E.rank()
The elliptic curves in class 6720bb have rank \(1\).
Complex multiplication
The elliptic curves in class 6720bb do not have complex multiplication.Modular form 6720.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.