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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 369600.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.a1 | 369600a2 | \([0, -1, 0, -2866753, 1280844577]\) | \(636113690544097576/195351319394847\) | \(800159004241293312000\) | \([2]\) | \(19660800\) | \(2.7157\) | |
| 369600.a2 | 369600a1 | \([0, -1, 0, 494647, 134607177]\) | \(26142012111575872/30453939069939\) | \(-15592416803808768000\) | \([2]\) | \(9830400\) | \(2.3691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.a have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.a do not have complex multiplication.Modular form 369600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
