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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 44880.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.a1 | 44880be1 | \([0, -1, 0, -4496, -137280]\) | \(-2454365649169/610929000\) | \(-2502365184000\) | \([]\) | \(114048\) | \(1.0970\) | \(\Gamma_0(N)\)-optimal |
| 44880.a2 | 44880be2 | \([0, -1, 0, 32464, 956736]\) | \(923754305147471/633316406250\) | \(-2594064000000000\) | \([]\) | \(342144\) | \(1.6463\) |
Rank
sage: E.rank()
The elliptic curves in class 44880.a have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.a do not have complex multiplication.Modular form 44880.2.a.a
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
