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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 17600dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.bc2 | 17600dd1 | \([0, -1, 0, -1793, 29857]\) | \(-19465109/22\) | \(-720896000\) | \([]\) | \(9216\) | \(0.61341\) | \(\Gamma_0(N)\)-optimal |
| 17600.bc3 | 17600dd2 | \([0, -1, 0, 12607, -310943]\) | \(6761990971/5153632\) | \(-168874213376000\) | \([]\) | \(46080\) | \(1.4181\) | |
| 17600.bc1 | 17600dd3 | \([0, -1, 0, -1940993, -1040206943]\) | \(-24680042791780949/369098752\) | \(-12094627905536000\) | \([]\) | \(230400\) | \(2.2228\) |
Rank
sage: E.rank()
The elliptic curves in class 17600dd have rank \(2\).
Complex multiplication
The elliptic curves in class 17600dd do not have complex multiplication.Modular form 17600.2.a.dd
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
