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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 135401c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135401.c3 | 135401c1 | \([1, -1, 0, -3101, -64008]\) | \(5545233/161\) | \(95766554681\) | \([2]\) | \(125440\) | \(0.88487\) | \(\Gamma_0(N)\)-optimal |
| 135401.c2 | 135401c2 | \([1, -1, 0, -7306, 150447]\) | \(72511713/25921\) | \(15418415303641\) | \([2, 2]\) | \(250880\) | \(1.2314\) | |
| 135401.c1 | 135401c3 | \([1, -1, 0, -104021, 12936170]\) | \(209267191953/55223\) | \(32847928255583\) | \([2]\) | \(501760\) | \(1.5780\) | |
| 135401.c4 | 135401c4 | \([1, -1, 0, 22129, 1039384]\) | \(2014698447/1958887\) | \(-1165191670803727\) | \([2]\) | \(501760\) | \(1.5780\) |
Rank
sage: E.rank()
The elliptic curves in class 135401c have rank \(0\).
Complex multiplication
The elliptic curves in class 135401c do not have complex multiplication.Modular form 135401.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
