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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 215950w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215950.h2 | 215950w1 | \([1, -1, 0, -424417, -108224259]\) | \(-541106281296959841/11321999360000\) | \(-176906240000000000\) | \([2]\) | \(2483712\) | \(2.1004\) | \(\Gamma_0(N)\)-optimal |
215950.h1 | 215950w2 | \([1, -1, 0, -6824417, -6860224259]\) | \(2249574551450240063841/955072563200\) | \(14923008800000000\) | \([2]\) | \(4967424\) | \(2.4470\) |
Rank
sage: E.rank()
The elliptic curves in class 215950w have rank \(0\).
Complex multiplication
The elliptic curves in class 215950w do not have complex multiplication.Modular form 215950.2.a.w
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.