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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 212160hh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.m2 | 212160hh1 | \([0, -1, 0, -1766375341, -47321371853795]\) | \(-595213448747095198927846967296/600281130562949295663181875\) | \(-614687877696460078759098240000\) | \([2]\) | \(247726080\) | \(4.4115\) | \(\Gamma_0(N)\)-optimal |
| 212160.m1 | 212160hh2 | \([0, -1, 0, -33140633841, -2321371551895695]\) | \(245689277968779868090419995701456/93342399137270122585475925\) | \(1529321867465033688440437555200\) | \([2]\) | \(495452160\) | \(4.7581\) |
Rank
sage: E.rank()
The elliptic curves in class 212160hh have rank \(1\).
Complex multiplication
The elliptic curves in class 212160hh do not have complex multiplication.Modular form 212160.2.a.hh
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.
