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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 92416.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92416.w1 | 92416l1 | \([0, 0, 0, -18050, 932824]\) | \(27000000/19\) | \(457662330368\) | \([2]\) | \(103680\) | \(1.1736\) | \(\Gamma_0(N)\)-optimal |
92416.w2 | 92416l2 | \([0, 0, 0, -14440, 1316928]\) | \(-216000/361\) | \(-556517393727488\) | \([2]\) | \(207360\) | \(1.5202\) |
Rank
sage: E.rank()
The elliptic curves in class 92416.w have rank \(0\).
Complex multiplication
The elliptic curves in class 92416.w do not have complex multiplication.Modular form 92416.2.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 LMFDB 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 LMFDB labels.