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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 60112.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60112.v1 | 60112t1 | \([0, -1, 0, -275224, -55477200]\) | \(23320116793/2873\) | \(284046277578752\) | \([2]\) | \(442368\) | \(1.7967\) | \(\Gamma_0(N)\)-optimal |
| 60112.v2 | 60112t2 | \([0, -1, 0, -252104, -65206096]\) | \(-17923019113/8254129\) | \(-816064955483754496\) | \([2]\) | \(884736\) | \(2.1433\) |
Rank
sage: E.rank()
The elliptic curves in class 60112.v have rank \(0\).
Complex multiplication
The elliptic curves in class 60112.v do not have complex multiplication.Modular form 60112.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
