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SageMath
E = EllipticCurve("kp1")
E.isogeny_class()
Elliptic curves in class 235200kp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.kp1 | 235200kp1 | \([0, -1, 0, -148633, -19869863]\) | \(140608/15\) | \(38739462720000000\) | \([2]\) | \(1720320\) | \(1.9173\) | \(\Gamma_0(N)\)-optimal |
| 235200.kp2 | 235200kp2 | \([0, -1, 0, 194367, -98416863]\) | \(39304/225\) | \(-4648735526400000000\) | \([2]\) | \(3440640\) | \(2.2639\) |
Rank
sage: E.rank()
The elliptic curves in class 235200kp have rank \(1\).
Complex multiplication
The elliptic curves in class 235200kp do not have complex multiplication.Modular form 235200.2.a.kp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
