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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 344760by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.by2 | 344760by1 | \([0, 1, 0, -74629358171, -12995818318743870]\) | \(-595213448747095198927846967296/600281130562949295663181875\) | \(-46359077816502699629611315886190000\) | \([2]\) | \(2601123840\) | \(5.3474\) | \(\Gamma_0(N)\)-optimal |
| 344760.by1 | 344760by2 | \([0, 1, 0, -1400191779796, -637510162918804720]\) | \(245689277968779868090419995701456/93342399137270122585475925\) | \(115339758652766121760429686802771200\) | \([2]\) | \(5202247680\) | \(5.6940\) |
Rank
sage: E.rank()
The elliptic curves in class 344760by have rank \(0\).
Complex multiplication
The elliptic curves in class 344760by do not have complex multiplication.Modular form 344760.2.a.by
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.
