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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 147294.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147294.v1 | 147294ck2 | \([1, -1, 0, -29556, -1278936]\) | \(33293019313/10932488\) | \(937637088639048\) | \([2]\) | \(829440\) | \(1.5759\) | |
147294.v2 | 147294ck1 | \([1, -1, 0, -11916, 488592]\) | \(2181825073/74816\) | \(6416678108736\) | \([2]\) | \(414720\) | \(1.2293\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147294.v have rank \(0\).
Complex multiplication
The elliptic curves in class 147294.v do not have complex multiplication.Modular form 147294.2.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.