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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 127449v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127449.b2 | 127449v1 | \([0, 0, 1, -297381, -67827650]\) | \(-28672/3\) | \(-304317292534477803\) | \([]\) | \(1741824\) | \(2.0938\) | \(\Gamma_0(N)\)-optimal |
127449.b1 | 127449v2 | \([0, 0, 1, -116275971, 482982999700]\) | \(-1713910976512/1594323\) | \(-161726686261815418104123\) | \([]\) | \(22643712\) | \(3.3763\) |
Rank
sage: E.rank()
The elliptic curves in class 127449v have rank \(2\).
Complex multiplication
The elliptic curves in class 127449v do not have complex multiplication.Modular form 127449.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.