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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 142956x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142956.bh2 | 142956x1 | \([0, 0, 0, 8664, -356668]\) | \(8192/11\) | \(-96578795453184\) | \([]\) | \(362880\) | \(1.3692\) | \(\Gamma_0(N)\)-optimal |
142956.bh1 | 142956x2 | \([0, 0, 0, -251256, -48753772]\) | \(-199794688/1331\) | \(-11686034249835264\) | \([]\) | \(1088640\) | \(1.9185\) |
Rank
sage: E.rank()
The elliptic curves in class 142956x have rank \(1\).
Complex multiplication
The elliptic curves in class 142956x do not have complex multiplication.Modular form 142956.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.