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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 14490.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.t1 | 14490v3 | \([1, -1, 0, -3895029, -2957816547]\) | \(8964546681033941529169/31696875000\) | \(23107021875000\) | \([2]\) | \(294912\) | \(2.2066\) | |
| 14490.t2 | 14490v4 | \([1, -1, 0, -324549, -12738195]\) | \(5186062692284555089/2903809817953800\) | \(2116877357288320200\) | \([2]\) | \(294912\) | \(2.2066\) | |
| 14490.t3 | 14490v2 | \([1, -1, 0, -243549, -46126395]\) | \(2191574502231419089/4115217960000\) | \(2999993892840000\) | \([2, 2]\) | \(147456\) | \(1.8600\) | |
| 14490.t4 | 14490v1 | \([1, -1, 0, -10269, -1196667]\) | \(-164287467238609/757170892800\) | \(-551977580851200\) | \([2]\) | \(73728\) | \(1.5134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14490.t have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.t do not have complex multiplication.Modular form 14490.2.a.t
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.
