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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3150.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.t1 | 3150o3 | \([1, -1, 0, -84042, -9356634]\) | \(5763259856089/5670\) | \(64584843750\) | \([2]\) | \(12288\) | \(1.3676\) | |
| 3150.t2 | 3150o2 | \([1, -1, 0, -5292, -142884]\) | \(1439069689/44100\) | \(502326562500\) | \([2, 2]\) | \(6144\) | \(1.0210\) | |
| 3150.t3 | 3150o1 | \([1, -1, 0, -792, 5616]\) | \(4826809/1680\) | \(19136250000\) | \([2]\) | \(3072\) | \(0.67446\) | \(\Gamma_0(N)\)-optimal |
| 3150.t4 | 3150o4 | \([1, -1, 0, 1458, -487134]\) | \(30080231/9003750\) | \(-102558339843750\) | \([2]\) | \(12288\) | \(1.3676\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.t have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.t do not have complex multiplication.Modular form 3150.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
