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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 23400d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.m2 | 23400d1 | \([0, 0, 0, -7575, -14649750]\) | \(-445090032/858203125\) | \(-92685937500000000\) | \([2]\) | \(221184\) | \(1.9346\) | \(\Gamma_0(N)\)-optimal |
| 23400.m1 | 23400d2 | \([0, 0, 0, -945075, -349337250]\) | \(216092050322508/3016755625\) | \(1303238430000000000\) | \([2]\) | \(442368\) | \(2.2812\) |
Rank
sage: E.rank()
The elliptic curves in class 23400d have rank \(0\).
Complex multiplication
The elliptic curves in class 23400d do not have complex multiplication.Modular form 23400.2.a.d
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.
