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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 242760.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242760.v1 | 242760v2 | \([0, -1, 0, -4612536, -3811303860]\) | \(219543018997682/5310375\) | \(262511704019712000\) | \([2]\) | \(6193152\) | \(2.4528\) | |
242760.v2 | 242760v1 | \([0, -1, 0, -277536, -64129860]\) | \(-95651055364/16734375\) | \(-413621382384000000\) | \([2]\) | \(3096576\) | \(2.1062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242760.v have rank \(0\).
Complex multiplication
The elliptic curves in class 242760.v do not have complex multiplication.Modular form 242760.2.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 LMFDB 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 LMFDB labels.