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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 2450v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2450.bd3 | 2450v1 | \([1, 0, 0, -148, -848]\) | \(-121945/32\) | \(-94119200\) | \([]\) | \(720\) | \(0.24686\) | \(\Gamma_0(N)\)-optimal |
| 2450.bd4 | 2450v2 | \([1, 0, 0, 1077, 6257]\) | \(46969655/32768\) | \(-96378060800\) | \([]\) | \(2160\) | \(0.79616\) | |
| 2450.bd2 | 2450v3 | \([1, 0, 0, -638, 73142]\) | \(-25/2\) | \(-2297832031250\) | \([]\) | \(3600\) | \(1.0516\) | |
| 2450.bd1 | 2450v4 | \([1, 0, 0, -153763, 23195017]\) | \(-349938025/8\) | \(-9191328125000\) | \([]\) | \(10800\) | \(1.6009\) |
Rank
sage: E.rank()
The elliptic curves in class 2450v have rank \(1\).
Complex multiplication
The elliptic curves in class 2450v do not have complex multiplication.Modular form 2450.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
