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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 92400.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.d1 | 92400bh2 | \([0, -1, 0, -7348, -234608]\) | \(1371324638864/34941753\) | \(1118136096000\) | \([2]\) | \(129024\) | \(1.0944\) | |
92400.d2 | 92400bh1 | \([0, -1, 0, 77, -11858]\) | \(24918016/30255687\) | \(-60511374000\) | \([2]\) | \(64512\) | \(0.74783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.d have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.d do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.