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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 70720bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70720.z1 | 70720bl1 | \([0, 0, 0, -1132, -6576]\) | \(611960049/282880\) | \(74155294720\) | \([2]\) | \(49152\) | \(0.78045\) | \(\Gamma_0(N)\)-optimal |
70720.z2 | 70720bl2 | \([0, 0, 0, 3988, -49584]\) | \(26757728271/19536400\) | \(-5121350041600\) | \([2]\) | \(98304\) | \(1.1270\) |
Rank
sage: E.rank()
The elliptic curves in class 70720bl have rank \(1\).
Complex multiplication
The elliptic curves in class 70720bl do not have complex multiplication.Modular form 70720.2.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.