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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 13328v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13328.u2 | 13328v1 | \([0, -1, 0, 24680, -297744]\) | \(3449795831/2071552\) | \(-998260823031808\) | \([2]\) | \(92160\) | \(1.5674\) | \(\Gamma_0(N)\)-optimal |
13328.u1 | 13328v2 | \([0, -1, 0, -100760, -2304784]\) | \(234770924809/130960928\) | \(63108801406042112\) | \([2]\) | \(184320\) | \(1.9139\) |
Rank
sage: E.rank()
The elliptic curves in class 13328v have rank \(0\).
Complex multiplication
The elliptic curves in class 13328v do not have complex multiplication.Modular form 13328.2.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.