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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 69360.dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69360.dh1 | 69360dq1 | \([0, 1, 0, -1745, -28650]\) | \(-127157223424/16875\) | \(-78030000\) | \([]\) | \(31104\) | \(0.53393\) | \(\Gamma_0(N)\)-optimal |
69360.dh2 | 69360dq2 | \([0, 1, 0, 295, -88422]\) | \(611926016/732421875\) | \(-3386718750000\) | \([]\) | \(93312\) | \(1.0832\) |
Rank
sage: E.rank()
The elliptic curves in class 69360.dh have rank \(0\).
Complex multiplication
The elliptic curves in class 69360.dh do not have complex multiplication.Modular form 69360.2.a.dh
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.