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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 86394.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86394.w1 | 86394w2 | \([1, 0, 1, -237883220, 1499323032722]\) | \(-840347716046483516416273/61875690788436630336\) | \(-109616560648853585274674496\) | \([]\) | \(37324800\) | \(3.7457\) | |
86394.w2 | 86394w1 | \([1, 0, 1, 16855660, 1534247570]\) | \(298954383299125345007/173578967063986176\) | \(-307505728470842413940736\) | \([]\) | \(12441600\) | \(3.1964\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86394.w have rank \(1\).
Complex multiplication
The elliptic curves in class 86394.w do not have complex multiplication.Modular form 86394.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.