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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 50025v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50025.e4 | 50025v1 | \([1, 0, 0, 1062, 24867]\) | \(8477185319/21880935\) | \(-341889609375\) | \([2]\) | \(46080\) | \(0.89688\) | \(\Gamma_0(N)\)-optimal |
| 50025.e3 | 50025v2 | \([1, 0, 0, -9063, 277992]\) | \(5268932332201/900900225\) | \(14076566015625\) | \([2, 2]\) | \(92160\) | \(1.2435\) | |
| 50025.e2 | 50025v3 | \([1, 0, 0, -41688, -3017133]\) | \(512787603508921/45649063125\) | \(713266611328125\) | \([2]\) | \(184320\) | \(1.5900\) | |
| 50025.e1 | 50025v4 | \([1, 0, 0, -138438, 19813617]\) | \(18778886261717401/732035835\) | \(11438059921875\) | \([2]\) | \(184320\) | \(1.5900\) |
Rank
sage: E.rank()
The elliptic curves in class 50025v have rank \(0\).
Complex multiplication
The elliptic curves in class 50025v do not have complex multiplication.Modular form 50025.2.a.v
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.
