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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 18240.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.t1 | 18240k4 | \([0, -1, 0, -194561, 33096705]\) | \(3107086841064961/570\) | \(149422080\) | \([2]\) | \(73728\) | \(1.4042\) | |
| 18240.t2 | 18240k3 | \([0, -1, 0, -14081, 346881]\) | \(1177918188481/488703750\) | \(128110755840000\) | \([2]\) | \(73728\) | \(1.4042\) | |
| 18240.t3 | 18240k2 | \([0, -1, 0, -12161, 520065]\) | \(758800078561/324900\) | \(85170585600\) | \([2, 2]\) | \(36864\) | \(1.0577\) | |
| 18240.t4 | 18240k1 | \([0, -1, 0, -641, 10881]\) | \(-111284641/123120\) | \(-32275169280\) | \([2]\) | \(18432\) | \(0.71109\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.t have rank \(0\).
Complex multiplication
The elliptic curves in class 18240.t do not have complex multiplication.Modular form 18240.2.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.
