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SageMath
E = EllipticCurve("jv1")
E.isogeny_class()
Elliptic curves in class 95550.jv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95550.jv1 | 95550jf4 | \([1, 0, 0, -105997438, -420049332508]\) | \(71647584155243142409/10140000\) | \(18640013437500000\) | \([2]\) | \(8847360\) | \(2.9749\) | |
| 95550.jv2 | 95550jf3 | \([1, 0, 0, -7605438, -4493660508]\) | \(26465989780414729/10571870144160\) | \(19433905477973122500000\) | \([2]\) | \(8847360\) | \(2.9749\) | |
| 95550.jv3 | 95550jf2 | \([1, 0, 0, -6625438, -6562440508]\) | \(17496824387403529/6580454400\) | \(12096623120400000000\) | \([2, 2]\) | \(4423680\) | \(2.6284\) | |
| 95550.jv4 | 95550jf1 | \([1, 0, 0, -353438, -133640508]\) | \(-2656166199049/2658140160\) | \(-4886367682560000000\) | \([2]\) | \(2211840\) | \(2.2818\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95550.jv have rank \(0\).
Complex multiplication
The elliptic curves in class 95550.jv do not have complex multiplication.Modular form 95550.2.a.jv
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.
