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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 355740.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.g1 | 355740g1 | \([0, -1, 0, -13312581, 38683468881]\) | \(-4890195460096/9282994875\) | \(-495304674867581195232000\) | \([]\) | \(44789760\) | \(3.2364\) | \(\Gamma_0(N)\)-optimal |
| 355740.g2 | 355740g2 | \([0, -1, 0, 114753819, -819604737279]\) | \(3132137615458304/7250937873795\) | \(-386881978760659712734145280\) | \([]\) | \(134369280\) | \(3.7857\) |
Rank
sage: E.rank()
The elliptic curves in class 355740.g have rank \(0\).
Complex multiplication
The elliptic curves in class 355740.g do not have complex multiplication.Modular form 355740.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
