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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 3136s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3136.p4 | 3136s1 | \([0, 0, 0, 196, 5488]\) | \(432/7\) | \(-13492928512\) | \([2]\) | \(1536\) | \(0.62435\) | \(\Gamma_0(N)\)-optimal |
| 3136.p3 | 3136s2 | \([0, 0, 0, -3724, 82320]\) | \(740772/49\) | \(377801998336\) | \([2, 2]\) | \(3072\) | \(0.97092\) | |
| 3136.p2 | 3136s3 | \([0, 0, 0, -11564, -378672]\) | \(11090466/2401\) | \(37024595836928\) | \([2]\) | \(6144\) | \(1.3175\) | |
| 3136.p1 | 3136s4 | \([0, 0, 0, -58604, 5460560]\) | \(1443468546/7\) | \(107943428096\) | \([2]\) | \(6144\) | \(1.3175\) |
Rank
sage: E.rank()
The elliptic curves in class 3136s have rank \(1\).
Complex multiplication
The elliptic curves in class 3136s do not have complex multiplication.Modular form 3136.2.a.s
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.
