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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 5040w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.m2 | 5040w1 | \([0, 0, 0, -108, 243]\) | \(442368/175\) | \(55112400\) | \([2]\) | \(1152\) | \(0.18380\) | \(\Gamma_0(N)\)-optimal |
5040.m1 | 5040w2 | \([0, 0, 0, -783, -8262]\) | \(10536048/245\) | \(1234517760\) | \([2]\) | \(2304\) | \(0.53038\) |
Rank
sage: E.rank()
The elliptic curves in class 5040w have rank \(1\).
Complex multiplication
The elliptic curves in class 5040w do not have complex multiplication.Modular form 5040.2.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.