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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 310464.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.bl1 | 310464bl2 | \([0, 0, 0, -9312528204, 345899169561456]\) | \(-61279455929796531/681472\) | \(-993252418080087899897856\) | \([]\) | \(209018880\) | \(4.1737\) | |
310464.bl2 | 310464bl1 | \([0, 0, 0, -108822924, 527470081264]\) | \(-71285434106859/18863581528\) | \(-37714490034001598937563136\) | \([]\) | \(69672960\) | \(3.6244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.bl do not have complex multiplication.Modular form 310464.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.