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SageMath
E = EllipticCurve("mg1")
E.isogeny_class()
Elliptic curves in class 331200mg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 331200.mg2 | 331200mg1 | \([0, 0, 0, 3300, 1026000]\) | \(574992/66125\) | \(-457056000000000\) | \([2]\) | \(884736\) | \(1.4924\) | \(\Gamma_0(N)\)-optimal |
| 331200.mg1 | 331200mg2 | \([0, 0, 0, -134700, 18414000]\) | \(9776035692/359375\) | \(9936000000000000\) | \([2]\) | \(1769472\) | \(1.8389\) |
Rank
sage: E.rank()
The elliptic curves in class 331200mg have rank \(2\).
Complex multiplication
The elliptic curves in class 331200mg do not have complex multiplication.Modular form 331200.2.a.mg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
