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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 30960bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.o1 | 30960bl1 | \([0, 0, 0, -22251963, -40299850262]\) | \(408076159454905367161/1190206406250000\) | \(3553937285760000000000\) | \([2]\) | \(2027520\) | \(3.0057\) | \(\Gamma_0(N)\)-optimal |
30960.o2 | 30960bl2 | \([0, 0, 0, -13251963, -73198450262]\) | \(-86193969101536367161/725294740213012500\) | \(-2165718489560211916800000\) | \([2]\) | \(4055040\) | \(3.3523\) |
Rank
sage: E.rank()
The elliptic curves in class 30960bl have rank \(0\).
Complex multiplication
The elliptic curves in class 30960bl do not have complex multiplication.Modular form 30960.2.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.