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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 72128r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.ca2 | 72128r1 | \([0, -1, 0, -515937, -142468255]\) | \(1969910093092/7889\) | \(60826121732096\) | \([2]\) | \(368640\) | \(1.8563\) | \(\Gamma_0(N)\)-optimal |
| 72128.ca1 | 72128r2 | \([0, -1, 0, -523777, -137906943]\) | \(1030541881826/62236321\) | \(959714548689010688\) | \([2]\) | \(737280\) | \(2.2029\) |
Rank
sage: E.rank()
The elliptic curves in class 72128r have rank \(1\).
Complex multiplication
The elliptic curves in class 72128r do not have complex multiplication.Modular form 72128.2.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.
