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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 115920cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.b1 | 115920cx1 | \([0, 0, 0, -23695293, 44395733783]\) | \(-126142795384287538429696/9315359375\) | \(-108654351750000\) | \([]\) | \(4250880\) | \(2.5895\) | \(\Gamma_0(N)\)-optimal |
| 115920.b2 | 115920cx2 | \([0, 0, 0, -23456793, 45333186383]\) | \(-122372013839654770813696/5297595236711512175\) | \(-61791150841003078009200\) | \([]\) | \(12752640\) | \(3.1388\) |
Rank
sage: E.rank()
The elliptic curves in class 115920cx have rank \(1\).
Complex multiplication
The elliptic curves in class 115920cx do not have complex multiplication.Modular form 115920.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
