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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 71478d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71478.ba2 | 71478d1 | \([1, -1, 0, 12387, 1218877]\) | \(165469149/603592\) | \(-766705969922904\) | \([]\) | \(518400\) | \(1.5390\) | \(\Gamma_0(N)\)-optimal |
71478.ba1 | 71478d2 | \([1, -1, 0, -604923, 181541987]\) | \(-26436959739/50578\) | \(-46835434141917894\) | \([]\) | \(1555200\) | \(2.0883\) |
Rank
sage: E.rank()
The elliptic curves in class 71478d have rank \(0\).
Complex multiplication
The elliptic curves in class 71478d do not have complex multiplication.Modular form 71478.2.a.d
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.