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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 143745.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143745.v1 | 143745m2 | \([0, 1, 1, -78377075, -267054103444]\) | \(15159227841150976/3026520525\) | \(10630591160932698228525\) | \([]\) | \(16111872\) | \(3.2251\) | |
| 143745.v2 | 143745m1 | \([0, 1, 1, -2397575, 929392031]\) | \(433937022976/144703125\) | \(508266753480662203125\) | \([3]\) | \(5370624\) | \(2.6758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 143745.v have rank \(0\).
Complex multiplication
The elliptic curves in class 143745.v do not have complex multiplication.Modular form 143745.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
