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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 38440h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38440.l2 | 38440h1 | \([0, -1, 0, -1241281736, 16833563535740]\) | \(-7812312501499996/244140625\) | \(-6609905540167750000000000\) | \([2]\) | \(17522688\) | \(3.8589\) | \(\Gamma_0(N)\)-optimal |
| 38440.l1 | 38440h2 | \([0, -1, 0, -19860656736, 1077311238285740]\) | \(15999976000011999998/15625\) | \(846067909141472000000\) | \([2]\) | \(35045376\) | \(4.2055\) |
Rank
sage: E.rank()
The elliptic curves in class 38440h have rank \(1\).
Complex multiplication
The elliptic curves in class 38440h do not have complex multiplication.Modular form 38440.2.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.
