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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 97104.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97104.j1 | 97104h4 | \([0, -1, 0, -633584, 194288160]\) | \(569001644066/122451\) | \(6053211057395712\) | \([4]\) | \(884736\) | \(2.0230\) | |
| 97104.j2 | 97104h3 | \([0, -1, 0, -286784, -57294432]\) | \(52767497666/1753941\) | \(86703865670510592\) | \([2]\) | \(884736\) | \(2.0230\) | |
| 97104.j3 | 97104h2 | \([0, -1, 0, -44024, 2327424]\) | \(381775972/127449\) | \(3150140448236544\) | \([2, 2]\) | \(442368\) | \(1.6765\) | |
| 97104.j4 | 97104h1 | \([0, -1, 0, 7996, 246624]\) | \(9148592/9639\) | \(-59561479063296\) | \([2]\) | \(221184\) | \(1.3299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97104.j have rank \(0\).
Complex multiplication
The elliptic curves in class 97104.j do not have complex multiplication.Modular form 97104.2.a.j
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.
