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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 30960v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.y2 | 30960v1 | \([0, 0, 0, -123, -22]\) | \(1860867/1075\) | \(118886400\) | \([2]\) | \(8192\) | \(0.23898\) | \(\Gamma_0(N)\)-optimal |
| 30960.y1 | 30960v2 | \([0, 0, 0, -1323, 18458]\) | \(2315685267/9245\) | \(1022423040\) | \([2]\) | \(16384\) | \(0.58555\) |
Rank
sage: E.rank()
The elliptic curves in class 30960v have rank \(1\).
Complex multiplication
The elliptic curves in class 30960v do not have complex multiplication.Modular form 30960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
