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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 155526db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.k1 | 155526db1 | \([1, 1, 0, -413816344, -3240280139060]\) | \(1311889499494111/438012\) | \(2616588239316550093476\) | \([2]\) | \(28385280\) | \(3.4677\) | \(\Gamma_0(N)\)-optimal |
155526.k2 | 155526db2 | \([1, 1, 0, -412001874, -3270100953510]\) | \(-1294708239486271/23981814018\) | \(-143262130984940092442951214\) | \([2]\) | \(56770560\) | \(3.8143\) |
Rank
sage: E.rank()
The elliptic curves in class 155526db have rank \(1\).
Complex multiplication
The elliptic curves in class 155526db do not have complex multiplication.Modular form 155526.2.a.db
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.