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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 155526da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.j1 | 155526da1 | \([1, 1, 0, -50530, 16176532]\) | \(-1967079625/14486688\) | \(-105082937100535968\) | \([]\) | \(1140480\) | \(1.9492\) | \(\Gamma_0(N)\)-optimal |
155526.j2 | 155526da2 | \([1, 1, 0, 449375, -408842699]\) | \(1383521234375/10764582912\) | \(-78083685453514309632\) | \([]\) | \(3421440\) | \(2.4985\) |
Rank
sage: E.rank()
The elliptic curves in class 155526da have rank \(1\).
Complex multiplication
The elliptic curves in class 155526da do not have complex multiplication.Modular form 155526.2.a.da
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.