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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 57600r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
|---|---|---|---|---|---|---|---|---|---|
| 57600.ch2 | 57600r1 | \([0, 0, 0, -750, -7000]\) | \(8000\) | \(5832000000\) | \([2]\) | \(27648\) | \(0.60348\) | \(\Gamma_0(N)\)-optimal | \(-8\) |
| 57600.ch1 | 57600r2 | \([0, 0, 0, -3000, 56000]\) | \(8000\) | \(373248000000\) | \([2]\) | \(55296\) | \(0.95005\) | \(-8\) |
Rank
sage: E.rank()
The elliptic curves in class 57600r have rank \(0\).
Complex multiplication
Each elliptic curve in class 57600r has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).Modular form 57600.2.a.r
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.
