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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 25200.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.ci1 | 25200c2 | \([0, 0, 0, -6707175, 6685741750]\) | \(308971819397054448/6565234375\) | \(709045312500000000\) | \([2]\) | \(737280\) | \(2.5427\) | |
| 25200.ci2 | 25200c1 | \([0, 0, 0, -404550, 112103875]\) | \(-1084767227025408/176547030625\) | \(-1191692456718750000\) | \([2]\) | \(368640\) | \(2.1961\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.ci do not have complex multiplication.Modular form 25200.2.a.ci
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.
