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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 18720h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18720.p1 | 18720h1 | \([0, 0, 0, -95313, 11305388]\) | \(2052450196928704/4317958125\) | \(201458654280000\) | \([2]\) | \(73728\) | \(1.6298\) | \(\Gamma_0(N)\)-optimal |
| 18720.p2 | 18720h2 | \([0, 0, 0, -62508, 19204832]\) | \(-9045718037056/48125390625\) | \(-143701646400000000\) | \([2]\) | \(147456\) | \(1.9764\) |
Rank
sage: E.rank()
The elliptic curves in class 18720h have rank \(0\).
Complex multiplication
The elliptic curves in class 18720h do not have complex multiplication.Modular form 18720.2.a.h
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.
