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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 2352.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2352.m1 | 2352k2 | \([0, -1, 0, -11384, 473712]\) | \(-16591834777/98304\) | \(-966770294784\) | \([]\) | \(4320\) | \(1.1401\) | |
| 2352.m2 | 2352k1 | \([0, -1, 0, 376, 3312]\) | \(596183/864\) | \(-8497004544\) | \([]\) | \(1440\) | \(0.59076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2352.m have rank \(0\).
Complex multiplication
The elliptic curves in class 2352.m do not have complex multiplication.Modular form 2352.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
