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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 23400.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.c1 | 23400bk4 | \([0, 0, 0, -1872075, -985900250]\) | \(31103978031362/195\) | \(4548960000000\) | \([2]\) | \(294912\) | \(2.0344\) | |
| 23400.c2 | 23400bk3 | \([0, 0, 0, -162075, -2470250]\) | \(20183398562/11567205\) | \(269839758240000000\) | \([2]\) | \(294912\) | \(2.0344\) | |
| 23400.c3 | 23400bk2 | \([0, 0, 0, -117075, -15385250]\) | \(15214885924/38025\) | \(443523600000000\) | \([2, 2]\) | \(147456\) | \(1.6878\) | |
| 23400.c4 | 23400bk1 | \([0, 0, 0, -4575, -422750]\) | \(-3631696/24375\) | \(-71077500000000\) | \([2]\) | \(73728\) | \(1.3413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23400.c have rank \(1\).
Complex multiplication
The elliptic curves in class 23400.c do not have complex multiplication.Modular form 23400.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
