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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 30345v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30345.i3 | 30345v1 | \([1, 0, 0, -96821, -11603880]\) | \(4158523459441/16065\) | \(387770045985\) | \([2]\) | \(110592\) | \(1.4371\) | \(\Gamma_0(N)\)-optimal |
| 30345.i2 | 30345v2 | \([1, 0, 0, -98266, -11240029]\) | \(4347507044161/258084225\) | \(6229525788749025\) | \([2, 2]\) | \(221184\) | \(1.7837\) | |
| 30345.i4 | 30345v3 | \([1, 0, 0, 73689, -46353240]\) | \(1833318007919/39525924375\) | \(-954059726890344375\) | \([2]\) | \(442368\) | \(2.1303\) | |
| 30345.i1 | 30345v4 | \([1, 0, 0, -293341, 47165426]\) | \(115650783909361/27072079335\) | \(653454182922036615\) | \([2]\) | \(442368\) | \(2.1303\) |
Rank
sage: E.rank()
The elliptic curves in class 30345v have rank \(0\).
Complex multiplication
The elliptic curves in class 30345v do not have complex multiplication.Modular form 30345.2.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.
