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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 53824.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53824.m1 | 53824d2 | \([0, -1, 0, -24491041, -46958951263]\) | \(-10418796526321/82044596\) | \(-12793161728084755349504\) | \([]\) | \(3225600\) | \(3.0705\) | |
| 53824.m2 | 53824d1 | \([0, -1, 0, 267999, 88607137]\) | \(13651919/29696\) | \(-4630478412950011904\) | \([]\) | \(645120\) | \(2.2658\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53824.m have rank \(1\).
Complex multiplication
The elliptic curves in class 53824.m do not have complex multiplication.Modular form 53824.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
