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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 158.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158.d1 | 158c2 | \([1, 1, 1, -23380, -1385691]\) | \(1413378216646643521/49232902384\) | \(49232902384\) | \([]\) | \(240\) | \(1.1421\) | |
158.d2 | 158c1 | \([1, 1, 1, -420, 3109]\) | \(8194759433281/82837504\) | \(82837504\) | \([5]\) | \(48\) | \(0.33739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 158.d have rank \(0\).
Complex multiplication
The elliptic curves in class 158.d do not have complex multiplication.Modular form 158.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.